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International Journal of Computing Science and Mathematics

 

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International Journal of Computing Science and Mathematics (29 papers in press)

 

Regular Issues

 

  • Vulnerability Analysis of Interaction-based Supply Chain Network and Its Self-organized Criticality   Order a copy of this article
    by Ren-Bin Xiao, Shanshan Xie, Tinggui Chen 
    Abstract: With the increasing complexity of the supply chain, it brings benefits as well as increasing vulnerability to the supply chain. Research on the cause and characteristic of vulnerability is prerequisite for effective management measures. First, a supply chain network model based on Possion distribution and preference selection mechanism was established, of which the interactions were further studied. On this basis, the cascading failure process of supply chain network was analyzed, and then the impact of supply chain network topology on the system vulnerability and the determination of node vulnerability were further discussed. Finally, an example of certain automotive group supply chain was used to verify the effectiveness and practicality of this method. The study found that the root of supply network vulnerability lies in cascading failure and there is a certain power-law relationship between its scale and frequency, namely supply chain network owns self-organized criticality, which affects the vulnerability of supply chain network. Meanwhile, the node vulnerability assessment method could provide an effective basis for taking preventive measures.
    Keywords: supply chain network; vulnerability; cascading failure; self-organized criticality(SOC)

  • An integrated resilient management approach to emergency logistics based on SOC   Order a copy of this article
    by Liang Geng, Ren-Bin Xiao, Ting-gui Chen 
    Abstract: As supply chain is becoming more vulnerable to disruptions, how to effectively prevent and respond to risks is a hot topic in supply chain management. In this paper, resilience management approach to supply chain risk control is applied, the practical problem of logistics distribution under the emergency environment is taken as an example and the implementation strategy of integrated resilience and its application effect are also discussed. This paper puts forward the integrated resilience management framework, which covers the early prevention, mid-term mitigation and later recovery. And it sets up resilience management mathematical model of logistics distribution and presents details about the implementation process of resilience strategy. The case study verified the effectiveness. Our method provides effective basis for resilience decision, which improves the real time capability and effectiveness of emergency logistics.
    Keywords: Resilience management; emergency logistics; SOC; Ant colony optimization.

  • A comparative study of finite element method for the numerical solution of reaction- diffusion problem   Order a copy of this article
    by Nini Maharana, Ameeya Kumar Nayak 
    Abstract: This paper presents a least-squares finite element approach for the solution of reaction- diffusion pellet problem for slab geometry by considering some special types of reactions which are applicable for chemical transformation of natural gas components. The nonlinear terms are treated with Newtons linearization technique. A detailed comparison with other weighted residual methods such as collocation, sub-domain and Galerkin methods are also examined. The issues related to chemical reactor problems and their error analysis is discussed both theoretically and numerically. The least-squares method suffers convergency effect by using the Picards method instead of Newtons iteration method as obtained by Galerkin and orthogonal collocation methods.
    Keywords: Least square method; weighted residuals; diffusion reaction equation; slab model.

  • K-Means clustering method based on artificial immune system in scientific research project management in Universities   Order a copy of this article
    by Yanmin Zhao, Shuai Chen, Tinggui Chen 
    Abstract: In order to solve the data analysis problem in scientific research management universities, this paper puts forward a K-Means clustering method based on artificial immune system. Firstly, the hidden rules and knowledge in the scientific data are found out in order to provide decision opinion for the development of education and scientific research. And then, the key research domain and creative characteristics of the subject can be obtained. Finally, the simulation results show that the method is feasible and effective.
    Keywords: K-Means clustering method; artificial immune system; the scientific research project management.

  • D-S Evidential Theory on sEMG Signal Recognition   Order a copy of this article
    by Weiliang Ding, Gongfa Li, Ying Sun, GuoZhang Jiang, Jianyi Kong, HongHai Liu 
    Abstract: In order to promote the accuracy and complexity in the recognition of sEMG signals by classifiers, this paper tells a method based on fused D-S evidential theory. Three features are discussed in the choice of parameters, which includes AR model coefficient, cepstral coefficients and time-domain integral absolute value. D-S evidential theory gets information based on information fusion of multi feature sets and multi classifiers. In recognition phase, many groups of data are used for the training and the rest is for the test. Through the compare of the accuracy in different parameters, the result is shown according to the experiment about the data fusion in D-S evidential theory. 6 actions is set to be the samples. According to three characters, the recognition accuracy is compared. The result shows that the fused data method of D-S evidential theory has better accuracy and robustness. The further study is to determine the optimal fusion feature set to make more accurate and higher robustness of the classification.
    Keywords: sEMG signal; D-S evidential theory; fused data; recognition.

  • A Framework for Generating Prioritized Test Scenarios using Firefly Optimization Technique   Order a copy of this article
    by Vikas Panthi, Durga Prasad Mohapatra 
    Abstract: The intention of this research is to generate test scenarios for concurrent and composite states in state machines using Firefly optimization algorithm. We have used state based coverage criterion such as state coverage, transition coverage, transition pair coverage etc. to evaluate the efficiency of our proposed algorithm. The proposed approach is useful for feasible test scenario generation. Generating exhaustive test scenarios for all concurrent interdependent sequences is exponential in size. As a result, in this paper, we find the important test scenarios in presence of concurrency in composite models.
    Keywords: Keywords: Test Scenario; Firefly Optimization Algorithm; State Machine Diagram; Coverage Criterion; Objective Function.

  • Computational method for one-dimensional heat equation subject to nonlocal conditions   Order a copy of this article
    by Mahmoud Behroozifar 
    Abstract: In this paper, a method based on Bernstein polynomial is proposed for numerical solution of an one-dimensional heat equation subject to nonlocal boundary conditions. Properties of Bernstein polynomial and operational matrices of integration, differentiation and the product are stated and utilized to reduce the solution of the given elliptic partial differential equation to the solution of the system of algebraic equations. Illustrative numerical tests are given to compare the efficiency and accuracy of the new method with other methods.
    Keywords: Heat equation; Nonlocal boundary conditions; Bernstein polynomial; Operational matrix; Numerical methods.

  • Numerical method for solving time-fractional multi-dimensional diffusion equations   Order a copy of this article
    by Amit Prakash, Manoj Kumar 
    Abstract: The key object of the current paper is to demonstrate a numerical technique to find the solution of fractional multi-dimensional diffusion equations that describe density dynamics in a material undergoing diffusion with the help of fractional variation iteration method (FVIM). Fractional variation iteration method is not confined to the minor parameter as usual perturbation method. This technique provides us analytical solution in the form of a convergent series with easily computable components. The advantage of this method over other method is that it does not require any linearization, perturbation and restrictive assumptions.
    Keywords: Fractional variational iteration method; Fractional multi-dimensional diffusion equations; He’s polynomials.

  • Research on Crawling mechanism and policy for crawling product information from Mobile Internet   Order a copy of this article
    by Chonghuan Xu, Shu Wang, Jia Chen 
    Abstract: Product information on the Mobile Internet grows fast in volume and becomes hard in acquisition. Companies tend to deliver product information on their well-tuned Mobile websites or websites that is responsive to various mobile devices. Thus, this kind of site is more of an web app than a traditional website, which we call a RIA(Rich Internet Application). With RIAs, information are kept secret from search engine spiders by means of HTML5, Ajax and other scripting techniques in deep web, user interactions are needed to trigger some prescribed events in some certain order to show the whole picture of the information we need. In this paper, we identified the crux of the problem is how to provide the mechanism to parse the scripts and manipulate DOM(Document Object Model) and the policy to trigger user events and run the scrape process. A new mechanism and policy was formulated based on web crawler techniques and studies in Ajax-specified web crawlers. By remodeling web pages redesigning the architecture of web crawler and refining scrape algorithm, we successfully scrape product data from Mobile Internet RIAs.
    Keywords: Crawler; Scrape data; Mobile Internet; RIA; Product information.

  • Algorithm and separating method for the optimisation of quadratic functions   Order a copy of this article
    by Belabbaci Amel, Djebbar Bachir 
    Abstract: This paper addresses the optimisation of quadratic functions on convex polyhedrons. We propose a method and an algorithm for optimising a strictly concave function. This algorithm uses a good initialisation by searching the nearest vertex of a convex set to an external point in order to surround the area where the optimal solution can be located. The optimal solution may be the nearest vertex found or a boundary point obtained by the projection of the critical point onto a separating hyperplane passing through the nearest vertex. This method and this algorithm can be adapted for the convex quadratic problem. In this case, the optimal solution is the farthest vertex from the critical point.
    Keywords: separating method; concave; quadratic function; vertex; convex, critical point; boundary point; maximising; separating hyperplane; optimisation.

  • A new type of negative customers   Order a copy of this article
    by Hasnaa EL MANDILI, Benayad NSIRI 
    Abstract: The possibility of removing a customer before being served is one that is often absent in the theory of random processes, most notably the theory of waiting queues. This reminds us of the concept of negative customer, which was set forth by three leading scientists: Gelenbe, Boucherie-Van Dijk, and Henderson. Negative customers are likely to eliminate positive (regular) ones and make them disappear. They cannot build up in the queue, and are simply lost if they arrive to an empty queue [1] [2]. In other contributions [3], we find a type of negative customer s that can build up in the queue, as opposed to Gelenbe negative customer s. After a comparison of the different kinds of negative customers, we introduce a new type of negative client, having the same properties mentioned above, but characterized by the fact that they may remove one or more regular clients, and leave the system after being server as a regular customer. We are interested in the case of systems with a single node server type M/M/1. We study the existence of stationary distribution, the intensity of transition, along with the quasi-reversibility of this new type of negative customer.
    Keywords: Queues; Quasi-reversibility; Stationary Distribution; Negative Clients; Transition Intensity.

  • Special sequences in weighted graphs   Order a copy of this article
    by Sunil Mathew, Jill K. Mathew 
    Abstract: In a weighted graph, the edges are mainly classified into α, β and δ. In this Paper, some sequences in weighted graphs are introduced. These concepts are based on the above classification. Characterizations of partial blocks and partial trees are obtained. It is shown that β sequence of a partial tree is the zero sequence, and α sequence of a partial block is a binary sequence.
    Keywords: graph; tree; sequence; partial block; partial tree.

  • An optimal order a posteriori parameter choice strategy with modified Newton iterative scheme for solving nonlinear ill-posed operator equations   Order a copy of this article
    by Rajan M P, Pradeep D 
    Abstract: Study of inverse problems are interesting and mathematically challenging due to the fact that in most of the situation they are unstable with respect to perturbations of the data. In this paper to solve such operator equations, we propose a modified form of Gauss-Newton method combined with an a posteriori parameter choice strategy with the inexact data. Convergence and the convergence rate results are proven. We consider both a-priori and a-posteriori choice rule of parameter that guarantees the scheme converges to the exact solution. The theoretical results are illustrated through numerical examples and compared with the standard scheme to demonstrate that the scheme is stable and achieves good computational output. The salient features of our proposed scheme are: (i) Convergence analysis and desired convergence rate require only weaker assumptions compared to many assumptions used in the standard scheme in literature; (ii) Consideration of an adaptive and numerically stable a posteriori parameter strategy that gives the same order of convergence as that of an a priori method; (iii) Computation of an optimal order regularization parameter of the order O(δ2/3) using a discrepancy principle.
    Keywords: Nonlinear Ill-posed Problems; Regularization; Iterative Method.

  • Adaptability-oriented hierarchical correlation optimization in product family design   Order a copy of this article
    by Xianfu Cheng, Junyi Luo, Dongshan Gao 
    Abstract: For leader-follower characteristic between platform parameters and customization parameters in product family design, a bi-level model and leader-follower correlation optimization model are developed. The adaptability of platform parameters is considered, and they are regarded as association parameters to transfer between the upper and lower in the model. After the values of platform variables in the upper level model are assigned, each sub-plan problem in the lower level model can be solved without relying on platform parameters under certain conditions. Simultaneously, incidence relation of platform parameters could be taken as relaxation constraints, and genetic algorithm is applied to solve the leader-follower correlation optimization model of the product family. Finally, an example on optimal design of product family for drum group is used to demonstrate the feasibility of the established model and proposed method.
    Keywords: Product family design; Product platform; Leader-follower correlation optimization; Adaptability; Genetic algorithm.

  • Block Triangular and Skew Symmetric Splitting Method for Steady State Vector of Linear System of Erogodic Block Circulant Markov Chains   Order a copy of this article
    by Ranadheer Donthi, Rajaiah Dasari, Mallareddy Perati 
    Abstract: In this paper, we determine steady state probability vector (pie) of erogodic block Circulant Markov chain using block triangular and skew symmetric method. The homogeneous system (pie)Q=0 is transformed to the non homogeneous regularized linear system Ax=b, and proved that the matrix A=Q^T+(epsilon)I is positive definite for (epsilon)>0 We applied block triangular and skew symmetric splitting method to compute steady state probability vector of regularized linear system whose coefficient matrix is block circulant stochastic rate matrix. The contraction factor (alpha) minimizes the spectral radius of block iteration matrix of block coefficient matrix A. To improve computing efficiency of the TSS iteration, we employ ITSS iteration. From the numerical results it is clear that the error of TSS iteration method converges rapidly compare to other existing methods.
    Keywords: Circulant stochastic matrices; Steady state probability vector; Block triangular matrix; Block skew symmetric matrix; TSS Method; Convergence analysis.

  • Task Allocation Algorithm for Virtual Design Organization in Agile Industrial Design   Order a copy of this article
    by Gangjun Yang, Xueliang Zhang 
    Abstract: Agile industrial design is a kind of modern industrial design method to deal with the rapid change of market demand. From the perspective of the development trend of industrial design, virtual design organization will be an important form of agile design organizations. Task allocation of organization members is the primary work of agile industrial design practice, and it will involve many complex factors. Innovation as the core of industrial design determines its agility. Firstly, the characteristics of industrial design in agile environment were analyzed in this paper. On the basis of this study, the influencing factors of virtual organization task allocation were discussed, and the task allocation factors for virtual organization were summarized into five aspects, namely, difficulty of innovation, interest degree, ability of comprehensive design, emergency degree of design task, and busy degree of design work. Based on these, the paper focused on the definition of the difficulty coefficient of design exploration, and the calculation method of influencing factors and task allocation algorithm were given, and the results were verified by an example.
    Keywords: Agile industrial design; task allocation algorithm; virtual design organization.

  • Heuristics for Single Machine Scheduling Problem with Family Setup Times   Order a copy of this article
    by Yunfang Peng, Yajuan Han, Yuyan Xiao, Saif Ullah 
    Abstract: Grouping of jobs from the same family on bottleneck resource is significant to reduce setup time of jobs. But, the grouping may result in delay of jobs. How to balance the contradiction between utilization of bottleneck resource and delivery time is a great challenge in production scheduling. This paper considers a single machine scheduling problem in which each job to be scheduled belongs to a family and family setup times exist. This paper is aimed to identify a schedule of families of jobs to minimize total tardiness with respect to the given due dates of the jobs. A mathematical model is formulated for this problem and a heuristic solution approach is presented. Computational experiments show that the proposed heuristic algorithm performs better both in terms of solution quality and computational time.
    Keywords: Single machine scheduling; Family; Setup time; Tardiness; Heuristic algorithm.

  • Digital equipment maintenance decision model and its application research for low carbon environment   Order a copy of this article
    by Li Renwang, Wu Xinli, Luo Qing, Song Jinyu, Liu Xinxia, Cai Ping 
    Abstract: Abstract:In order to improve the resources and energy efficiency of digital device during the repair process, this paper take selected phase of S layer maintenance mode as device important degree analysis, considering the impact of environment during the repair process, use the modified fuzzy comprehensive evaluation method to describe the various elements of criticality for comprehensive evaluation, establish the digital equipment maintenance decision model for low-carbon environment; combine the qualitative and quantitative analysis to determine the level of membership evaluation factors, use the quasi excellent consistent matrix and variable weight comprehensive to improve the conventional weights, then, select the appropriate comprehensive evaluation model for solving the criticality, use the logic method to determine maintenance mode based on the degree of importance. Finally verify the correctness and practicability of the model by through an example.
    Keywords: Keywords: digital equipment; low carbon environment; maintenance decision.

  • Study on Clustering of Micro-Blog Business Enterprise Users Reputation Based on Web Crawler   Order a copy of this article
    by Meiyu Fang, Qibei Lu 
    Abstract: Micro-blog is a social tool of the new network era. It swept the world with its convenience of usage and real time release of information. PageRank and Hits algorithms are the most widely used method in the evaluation of Micro-Blogs influence. But the two algorithms have the deficiency of poor performance and unrelated to specified keywords. We proposed a Micro-blog enterprise users reputation analysis model based on clustering network and improved PageRank algorithm. The model was simulated with the Sina micro-blog data acquired by web crawler, and the model were compared with Hits and PageRank algorithm. The results show that the model has better convergence and its computational efficiency is superior to the traditional evaluation model based on PageRank or Hits algorithm.
    Keywords: Web crawler; E-commerce; Micro-blog.

  • Modular and homomorphic product of intuitionistic fuzzy graphs and their degree   Order a copy of this article
    by Sankar Sahoo, Madhumangal Pal 
    Abstract: An intuitionistic fuzzy graph is an extension of a fuzzy graph that give more precision, flexibility and compatibility to a system when compared with the system that designed using fuzzy graphs. In this paper, we define two new operations on intuitionistic fuzzy graphs, namely modular product and homomorphic product and study about the degree of the vertex of the resultant graph, which are obtained from two intuitionistic fuzzy graphs $G^prime$ and $G^{primeprime}$ using the operations modular product and homomorphic product. These operations will be used in computer science, geometry, algebra, operations research, etc.
    Keywords: Intuitionistic fuzzy graphs; modular product; homomorphic product.

  • A New Local-enhanced Cuckoo Search Algorithm   Order a copy of this article
    by Weihong YANG 
    Abstract: Cuckoo search algorithm is a recent proposed evolutionary algorithm. However, the local search capability is not efficient whenrndealing with some multi-modal numerical problems. In this paper, a new local-enhanced cuckoo search algorithm is designed aiming tornsolve it. Different from the standard version, the local search for each cuckoo is attracted by global best position found by entire swarm.rnFurthermore, to provide a balance between exploitation and exploration, a inertia weight is introduced. To test the performance, four otherrnalgorithms are employed to compare, and simulation results show it achieves the best performance when solve numerical optimizationrnbenchmarks.
    Keywords: Cuckoo search algorithm; local search pattern; inertia weight.

  • An Exponential Function Inflation Size of Multi-verse Optimization Algorithm for Global Optimization   Order a copy of this article
    by Yongquan Zhou, Wei Pan, Zhiming Li 
    Abstract: This paper proposed an improved multi-verse optimization (IMVO) algorithm based on exponential function inflation size. The main inspirations of IMVO are based on cosmic expansion, and inflation never ends. In the entire universe, we can think it is exponential growth. Exponential function inflation size is introduced to enhance accuracy and increase convergence rate of the multi-verse optimization (MVO) algorithm. The numerical simulation experiments and comparisons are carried out based on a set of 10 benchmark functions. The IMVO algorithm is compared with multi-verse optimization (MVO), moth-flame optimization (MFO), artificial bee colony (ABC) algorithm, bat algorithm (BA), differential evolution (DE) algorithm and dragonfly algorithm (DA). The experiment results show that the IMVO has not only the higher accuracy but also the faster convergence speed.
    Keywords: Exponential inflation size; multi-verse optimization; improved multi-verse optimization benchmark functions; meta-heuristic.

  • The structural topology optimization based on parameterized level-set method in Isogeometric analysis   Order a copy of this article
    by Zijun Wu, Shuting Wang 
    Abstract: The Isogeometric analysis(IGA), which establishes a bridge between CAD and CAE, offers a new convenient framework of optimization. This article develops an approach to apply the non-uniform rational basis splines(NURBS) based IGA to the topology optimization using parameterized level set method. Here, the objective function is evaluated according to the basis function of NURBS and the level set function is constructed through collocation points using the compactly supported radial basis function. To evaluate the equivalent strain energy for each elements, the level-set function value of every node is calculated from the corresponding value of collocation points. We have compared the numerical result accuracy as well as the time cost of the proposed method, and it turns out to be very promising.
    Keywords: Isogeometric analysis; Topology optimization; Level set method; Radial basis functions.

  • Solving Systems of Nonlinear Equations via Conjugate Direction Flower Pollination Algorithm   Order a copy of this article
    by Mohamed Abdelbaset, Ibrahim Hezam 
    Abstract: In this paper, we propose a new hybrid algorithm for solving system of nonlinear equations. The aim of hybridization is to utilize the feature of flower pollination algorithm (FPA) and conjugate direction method CD. conjugate direction flower pollination algorithm (CDFPA) combine the advantages of CD and FPA. The problem of solving nonlinear equations is equivalently changed to the problem of function optimization, and then a solution is obtained by CDFPA. The results show the proposed algorithm has high convergence speed and accuracy for solving nonlinear equations.
    Keywords: Flower pollination algorithm; Meta-heuristics; Optimization; Conjugate direction method; Nonlinear Equations.

  • An encoding and reconstructing method with robust transmission for 3D model topological data over wireless network   Order a copy of this article
    by Huiqin Wang, Bailin Yang 
    Abstract: This paper proposes an encoding and reconstructing method with robust transmission for 3D model topological data. For the encoding of topological data, we firstly adopt the valence-driven method to visit the full mesh and give each vertex a sequence number, degree information and the neighboring vertex information. Then, we adopt the improved graph coloring algorithm to color each vertex according to the sequence number of vertex. Thirdly, we divide the 3D model into several packets according to vertexs color. Finally, we use the Huffman coding to compress model. For the reconstructing of topological data, when the client receives packets, we design an effective reconstructing method by combining degree information, the neighboring vertex information with special traversal rule to reconstruct the model. Experimental results show that even in the high packet loss rate, the model can also obtain a good reconstruction result.
    Keywords: Topological data encoding; Model reconstructing; Graph coloring; Wireless network; Model Transmission.

  • The most suitable scheme selection of mechanical product configuration based on multi-objective decision analysis   Order a copy of this article
    by Bo Wei, Renwang Li, Gang Chen 
    Abstract: In the process of mechanical product configuration, if there is more than one feasible scheme, it is required to choose the one which is most consistent with the actual conditions of core enterprise. These actual conditions include cost, quality, delivery time and other factors that are related to the interests of the core enterprise. We propose to find the most suitable scheme from the feasible scheme set by using data envelopment analysis. By comparing the projected variable and the original data, we also know how much improvement can be achieved for a specific scheme. The above algorithm is verified and illustrated using a case study.
    Keywords: carbon footprint; multi-objective decision-making; product configuration; data envelopment analysis.

  • Randomness of Lacunary statistical acceleration convergence of $Gamma^{3}$ over $p-$ metric spaces defined by Orlicz functions   Order a copy of this article
    by Nagarajan Subramanian 
    Abstract: In this article the notion of Randomness of Lacunary statistical acceleration convergence of $Gamma^{3}$ over $p-$ metric spaces defined by sequence of Orlicz has been introduced and some theorems related to that concept have been established using the four dimensional matrix transformations. Author's construction with new definitions and also new statement of theorems of proofs are formulated. rn\textbf{keywords :} analytic sequence, double sequences, $Gamma^{3}$ space, Musielak - Orlicz function, Random $p-$ metric space, Lacunary sequence, Statistical convergence, Converging faster, Converging at the same rate, Acceleration field, triple natural density.
    Keywords: analytic sequence; double sequences; $Gamma^{3}$ space; Musielak - Orlicz function; Random $p-$ metric space; Lacunary sequence; Statistical convergence; Converging faster; Converging at the same rate; Acceleration field; triple natural density.

  • Generalized triple difference of rough intuitionistic statistical convergence in probability of fractional order defined by Musielak-Orlicz function   Order a copy of this article
    by Nagarajan Subramanian 
    Abstract: We generalized the concepts in probability of rough intuitionistic convergence and rough intuitionistic statistically convergence by introducing the generalized difference operator $Delta^{alpha}_{gamma}$ of fractional order, where $alpha$ is a proper fraction and $gamma=left(gamma_{mnk}right)$ is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator and investigate the topological structures of related of triple difference sequence spaces of $chi^{3}_{f}left(Delta^{alpha}_{gamma}x_{mnk}right)$.rnindent The main focus of the present paper is to generalized rough intuitionistic convergence and rough intuitionistic statistical difference of triple difference sequence spaces of $chi^{3}$ and investigate their topological structures as well as some interesting results concerning the operator $Delta^{alpha}_{gamma}.$ rn
    Keywords: analytic sequence; Orlicz function; triple sequences; chi sequence; intuitionistic; statistical convergence,Ces$acute{a}$ro $C_{1,1,1}-$ statistical convergence.

  • Bratu-like equation arising in electrospinning process: a Green's function fixed-point iteration approach   Order a copy of this article
    by Suheil Khuri, Ali Sayfy, Heba Kafri 
    Abstract: The aim of this article is to solve a Bratu-like nonlinear differential equation arising in electrospinning and vibration-electrospinningrn process that was recently introduced by Liu and Wang (2014). Electro-spinning process has been associated to Bratu equation through thermo-electro-hydrodynamics balance equations. The proposed strategy is based on embedding Green's function into Picard's fi xed point iteration scheme. Validation of the novel algorithm is demonstrated through numerical examples which comprise certain selected values of the parameters that appear in the modeled equation.
    Keywords: Bratu-like equation; electrospinning process; Green's functions; fixed-point iterations.