Most recent issue published online in the International Journal of Mathematical Modelling and Numerical Optimisation.
International Journal of Mathematical Modelling and Numerical Optimisation
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International Journal of Mathematical Modelling and Numerical Optimisation
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International Journal of Mathematical Modelling and Numerical Optimisation
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http://www.inderscience.com/browse/index.php?journalID=352&year=2023&vol=13&issue=4
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Adaptive finite element method for wick stochastic partial differential equations
http://www.inderscience.com/link.php?id=134153
In this paper we approximate the solution of the wick stochastic partial differential equation by the affine conforming finite element method. Then we provide a priori and a posteriori error estimations and prove the convergence of the numerical method. In particular, we construct a Galerkin approximation scheme and we derive the local residual based on posteriori error indicator, all the while proving its efficiency and reliability. Finally, two numerical examples are presented and analysed to illustrate the derived theoretical results, the effectiveness of the proposed adaptive algorithm and the good behaviour of the numerical solution and the mesh adaptation strategy used.
Adaptive finite element method for wick stochastic partial differential equations
Boujemâa Achchab; Khalid Bouihat; Abderrezzak El-Bouayadi
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 13, No. 4 (2023) pp. 327 - 351
In this paper we approximate the solution of the wick stochastic partial differential equation by the affine conforming finite element method. Then we provide a priori and a posteriori error estimations and prove the convergence of the numerical method. In particular, we construct a Galerkin approximation scheme and we derive the local residual based on posteriori error indicator, all the while proving its efficiency and reliability. Finally, two numerical examples are presented and analysed to illustrate the derived theoretical results, the effectiveness of the proposed adaptive algorithm and the good behaviour of the numerical solution and the mesh adaptation strategy used.]]>
10.1504/IJMMNO.2023.134153
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 13, No. 4 (2023) pp. 327 - 351
Boujemâa Achchab
Khalid Bouihat
Abderrezzak El-Bouayadi
Laboratory of Analysis and Modeling Systems for Decision Support, Department of Mathematics Computer Engineering, ENSA, Hassan 1st University, B.P. 218, Berrechid 26100, Morocco; Mohammed VI Polytechnic University, Ben Guerir, Morocco ' Laboratory of Analysis and Modeling Systems for Decision Support, Department of Mathematics Computer Engineering, ENSA, Hassan 1st University, B.P. 218, Berrechid 26100, Morocco ' Laboratory of Analysis and Modeling Systems for Decision Support, Department of Mathematics Computer Engineering, ENSA, Hassan 1st University, B.P. 218, Berrechid 26100, Morocco
wick stochastic equation? finite element method? a posteriori error estimation? error indicators? adaptive meshes
2023-10-12T23:20:50-05:00
Copyright © 2023 Inderscience Enterprises Ltd.
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327
351
2023-10-12T23:20:50-05:00
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Optimising reactive power using a hybrid improved shuffled bat algorithm
http://www.inderscience.com/link.php?id=134157
One well-known example of a challenging mixed-integer nonlinear optimisation problem is the problem of optimum reactive power dispatch. The bats analyse the echo to determine the position of their prey as well as its size before continuing on their hunt. We compare the outcomes of our technique to those of other bio-inspired algorithms, like the biogeography-based optimisation (BBO) algorithm, to determine its effectiveness. The suggested strategy has the potential to be more successful than almost all of existing methods in terms of having lower minimum values and lower maximum values for the control parameters, according to comparisons of the findings. Bus no. 29 now has a solar power generation system, resulting in an additional 0.3 kW loss reduction. The simulation findings suggest that the bat optimisation algorithm (BOA) is more effective than the other algorithms tested from the research.
Optimising reactive power using a hybrid improved shuffled bat algorithm
J. Gowrishankar; G. Balasundaram; J. Manikandan; D. Chandrakala; P. Munisekhar
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 13, No. 4 (2023) pp. 352 - 364
One well-known example of a challenging mixed-integer nonlinear optimisation problem is the problem of optimum reactive power dispatch. The bats analyse the echo to determine the position of their prey as well as its size before continuing on their hunt. We compare the outcomes of our technique to those of other bio-inspired algorithms, like the biogeography-based optimisation (BBO) algorithm, to determine its effectiveness. The suggested strategy has the potential to be more successful than almost all of existing methods in terms of having lower minimum values and lower maximum values for the control parameters, according to comparisons of the findings. Bus no. 29 now has a solar power generation system, resulting in an additional 0.3 kW loss reduction. The simulation findings suggest that the bat optimisation algorithm (BOA) is more effective than the other algorithms tested from the research.]]>
10.1504/IJMMNO.2023.134157
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 13, No. 4 (2023) pp. 352 - 364
J. Gowrishankar
G. Balasundaram
J. Manikandan
D. Chandrakala
P. Munisekhar
Department of Electrical and Electronics Engineering, Siddharth Institute of Engineering & Technology (Autonomous), Puttur, Andhra Pradesh, India ' Department of Electrical and Electronics Engineering, Sri Venkateswara College of Engineering and Technology (Autonomous), Chittoor, Andhra Pradesh, India ' Department of Computing Science and Engineering, VIT Bhopal University, Sehore, Bhopal, 466114, India ' Department of Electrical and Electronics Engineering, Easwari Engineering College, Chennai, 600089, India ' Department of Electrical and Electronics Engineering, Siddharth Institute of Engineering and Technology, Puttur, AP, India
optimisation optimal power system dispatch
solar grids
the bat algorithm
whale optimisation
microgrids
ORPD
2023-10-12T23:20:50-05:00
Copyright © 2023 Inderscience Enterprises Ltd.
13
4
352
364
2023-10-12T23:20:50-05:00
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A robust semi-analytical approach to study fractional coupled Sokolov Wilson system in shallow water waves
http://www.inderscience.com/link.php?id=134155
In this paper, a semi-analytical approach namely, modified differential transform method is suggested to investigate coupled fractional nonlinear Drinfeld-Sokolov-Wilson equations (CFDSWE) that arise in shallow water flow models. The Caputo sense is used to characterise the fractional derivative. The solution of coupled fractional nonlinear Drinfeld-Sokolov-Wilson equations is obtained for two different cases. The obtained solution shows an excellent agreement with the exact solution for classical order which shows the effectiveness and reliability of the method. The results show that the fractional modified differential transform method is a promising tool to find the analytical solution of highly nonlinear fractional PDEs. The computational work is done in the MATLAB software package.
A robust semi-analytical approach to study fractional coupled Sokolov Wilson system in shallow water waves
Yogeshwari F. Patel; Jayesh M. Dhodiya
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 13, No. 4 (2023) pp. 365 - 382
In this paper, a semi-analytical approach namely, modified differential transform method is suggested to investigate coupled fractional nonlinear Drinfeld-Sokolov-Wilson equations (CFDSWE) that arise in shallow water flow models. The Caputo sense is used to characterise the fractional derivative. The solution of coupled fractional nonlinear Drinfeld-Sokolov-Wilson equations is obtained for two different cases. The obtained solution shows an excellent agreement with the exact solution for classical order which shows the effectiveness and reliability of the method. The results show that the fractional modified differential transform method is a promising tool to find the analytical solution of highly nonlinear fractional PDEs. The computational work is done in the MATLAB software package.]]>
10.1504/IJMMNO.2023.134155
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 13, No. 4 (2023) pp. 365 - 382
Yogeshwari F. Patel
Jayesh M. Dhodiya
Department of Mathematical Sciences, P.D. Patel Institute of Applied Sciences, Charotar University of Science and Technology, Changa, Anand, Gujarat-388421, India ' Department of Mathematics, Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat-395007, India
shallow water waves? modified differential transform method? fractional coupled partial differential equation? coupled Sokolov Wilson system
2023-10-12T23:20:50-05:00
Copyright © 2023 Inderscience Enterprises Ltd.
13
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365
382
2023-10-12T23:20:50-05:00
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Post COVID-19 dynamics through fractional-order
http://www.inderscience.com/link.php?id=134154
In this article, a fractional-order model for the COVID-19 scenario in India is formulated using nine different compartments in the Caputo sense. The fractional-order model mainly focuses on memory giving a better understanding of results. The formulated model has three equilibrium points namely disease-free, asymptomatic-free, and endemic equilibria. The basic reproduction number is computed for the model. The local stability conditions are derived for all three equilibrium points. Also, after four lockdowns in India, in this study, the unlocked COVID-19 data is considered for the best fit using the least curve fit method shown in numerical simulation. The figures and graphs are plotted to show the effectiveness of fractional-order and other various dynamics of the system.
Post COVID-19 dynamics through fractional-order
Nita H. Shah; Nisha Sheoran
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 13, No. 4 (2023) pp. 383 - 404
In this article, a fractional-order model for the COVID-19 scenario in India is formulated using nine different compartments in the Caputo sense. The fractional-order model mainly focuses on memory giving a better understanding of results. The formulated model has three equilibrium points namely disease-free, asymptomatic-free, and endemic equilibria. The basic reproduction number is computed for the model. The local stability conditions are derived for all three equilibrium points. Also, after four lockdowns in India, in this study, the unlocked COVID-19 data is considered for the best fit using the least curve fit method shown in numerical simulation. The figures and graphs are plotted to show the effectiveness of fractional-order and other various dynamics of the system.]]>
10.1504/IJMMNO.2023.134154
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 13, No. 4 (2023) pp. 383 - 404
Nita H. Shah
Nisha Sheoran
Department of Mathematics, Gujarat University, Ahmedabad-380009, Gujarat, India ' Department of Mathematics, Gujarat University, Ahmedabad-380009, Gujarat, India
COVID-19
basic reproduction number
equilibrium points
local stability
Caputo derivative
sensitivity analysis
least curve fit
2023-10-12T23:20:50-05:00
Copyright © 2023 Inderscience Enterprises Ltd.
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383
404
2023-10-12T23:20:50-05:00
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Computational models to study the infectious disease COVID-19: a review
http://www.inderscience.com/link.php?id=134156
The current COVID-19 pandemic that is still waging in the world is a threat to humanity, and the cure for it is a big challenge for researchers, scientists, and the bio-medical community. However, the vaccine is available nowadays, but the infection is still increasing globally. In this paper, the different types of existing mathematical models related to the COVID-19 outbreak, namely, SI, SIS, SEIS, SIR, SIRS, SEIR, AI, logistic growth model, Poisson model and the expanded models are discussed. The basic reproduction number is one of the most important parameters for predicting the future of COVID-19, and existing models use it to forecast coronavirus disease around the globe. The motive of present study is to elaborate the key factors related to control of pandemic and to introduce the different type of existing mathematical models and applications to the readers under one platform. The initial description of the existing mathematical models gives us better insight of the disease and based on existing literature, future prediction of the spread of COVID-19 can be done more accurately and efficiently.
Computational models to study the infectious disease COVID-19: a review
Amit Sharma; Gaurang Sharma; Fateh Singh
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 13, No. 4 (2023) pp. 405 - 441
The current COVID-19 pandemic that is still waging in the world is a threat to humanity, and the cure for it is a big challenge for researchers, scientists, and the bio-medical community. However, the vaccine is available nowadays, but the infection is still increasing globally. In this paper, the different types of existing mathematical models related to the COVID-19 outbreak, namely, SI, SIS, SEIS, SIR, SIRS, SEIR, AI, logistic growth model, Poisson model and the expanded models are discussed. The basic reproduction number is one of the most important parameters for predicting the future of COVID-19, and existing models use it to forecast coronavirus disease around the globe. The motive of present study is to elaborate the key factors related to control of pandemic and to introduce the different type of existing mathematical models and applications to the readers under one platform. The initial description of the existing mathematical models gives us better insight of the disease and based on existing literature, future prediction of the spread of COVID-19 can be done more accurately and efficiently.]]>
10.1504/IJMMNO.2023.134156
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 13, No. 4 (2023) pp. 405 - 441
Amit Sharma
Gaurang Sharma
Fateh Singh
Department of Mathematics, Shri P.N. Pandya Arts, M.P. Pandya Science and Smt. D.P. Pandya Commerce College, Lunawada-389230, Gujarat, India; Shri Govind Guru University, Godhra-388713, Gujarat, India ' Department of Mathematics, Shri P.N. Pandya Arts, M.P. Pandya Science and Smt. D.P. Pandya Commerce College, Lunawada-389230, Gujarat, India; Shri Govind Guru University, Godhra-388713, Gujarat, India ' Department of Mathematics, DIT University, Dehradun, Uttarakhand-248009, India
mathematical model? logistic growth model? Poisson model? COVID-19
2023-10-12T23:20:50-05:00
Copyright © 2023 Inderscience Enterprises Ltd.
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405
441
2023-10-12T23:20:50-05:00