International Journal of Mathematical Modelling and Numerical Optimisation (17 papers in press)

Regular Issues

• Open Access

  Numerical modelling of wave propagation in shallow water ( Free Full-text Access )

  by Vetrichelvan Pugazendi, Efstratios L. Ntantis 
  Abstract: Coastal communities worldwide face significantly higher risks than their inland counterparts, primarily due to threats like tsunamis, dam failures, and storm surges. Identifying and addressing these hazards before they result in loss of life is paramount. This paper presents a numerical scheme developed in MATLAB to solve shallow water equations, offering a valuable tool for mitigating these critical threats. Traditionally, computational limitations in memory and speed have required the division of complex simulations into smaller, more manageable sections in computational fluid dynamics. While advancements in computational power have grown exponentially, so too has the complexity of the problems being addressed. The model employs finite difference methods to solve the shallow water equations, utilising user-defined parameters such as domain size, shape, grid resolution, and boundary conditions. It generates customised data and presents results through animated visualisations. The results from this model have shown promising potential, highlighting its ability to enhance understanding and mitigation strategies for coastal hazards significantly.
  Keywords: coastal hazards; coastal fluid dynamics; mitigation strategies; shallow water equations; MATLAB simulation.
  DOI: 10.1504/IJMMNO.2025.10073051
   
  
• Structure preserving numerical analysis of HIV/AIDS epidemic model  
  by Shah Zeb, Muhammad Bilal, Muhammad Rafiq, Siti Ainor Mohd Yatim, Zulfiqar Ali, Ayesha Kamran 
  Abstract: Human immunodeficiency virus (HIV) remains a major global health concern. This study presents a mathematical model using ordinary differential equations with a saturated incidence rate to analyse HIV transmission dynamics. The basic reproduction number R0 is derived, indicating disease-free equilibrium stability when R0<1, and endemic stability when R0 >1. Unlike conventional models, we employ structure-preserving numerical schemes to ensure biologically consistent solutions and unconditional stability. Two numerical approaches are developed: the standard finite difference (SFD) and non-standard finite difference (NSFD) methods. While SFD shows conditional convergence, the NSFD scheme provides unconditionally stable and positive solutions, even with large time steps. Numerical experiments confirm the accuracy and practicality of the proposed NSFD approach. This model and method can be extended to other infectious diseases, such as hepatitis and whooping cough, offering a robust tool for long-term epidemiological analysis and control strategy assessment.
  Keywords: human immunodeficiency virus; HIV; basic reproduction number; standard finite difference; SFD; non-standard finite difference; NSFD; stability analysis; comparison.
  DOI: 10.1504/IJMMNO.2025.10071899
   
  
• The new family of Ristić-Balakrishnan-type II Topp-Leone-heavy-tailed-G distribution with applications  
  by Oarabile Lekhane, Broderick Oluyede, Lesego Gabaitiri, Onkabetse Vincent Mabikwa 
  Abstract: We propose the new Ristić-Balakrishnan-type II Topp-Leone-heavy-tailed-G distribution. Some properties are derived including linear representation of the density function, probability weighted moments, R ényi entropy and distribution of order statistics. Several estimation methods are compared via simulation studies to establish the best method for parameter estimation of the new family of distributions. Actuarial measures are discussed and numerical studies are conducted to characterise the new family of distributions as heavy-tailed and its performance is validated using real data.
  Keywords: Ristić-Balakrishnan; type II Topp-Leone; heavy-tailed; simulation.
  DOI: 10.1504/IJMMNO.2025.10072140
   
  
• Mixed convection with heating effects through a vertical pipe in the presence of magnetic field  
  by Saurabh Kapoor, Durgaprasad Nayak 
  Abstract: This manuscript addresses the impact of magnetic field in the mixed convective flow through a vertical pipe in a porous medium along with heat source effect. We have used the non-Darcy-Brinkman-Forchheimer (NDBF) extended model to describe the flow in porous medium. The solutions for the coupled differential equations have been obtained using the Chebyshev spectral-collocation approach. It is demonstrated that under the limiting conditions the present numerical results agree well with the existing numerical data. The primary aim of this study is to investigate the influence of multiple parameters, including heat source effect, magnetic field, Forchheimer number and Darcy number on both velocity and temperature profiles. Key findings show that increasing the magnetic field strength results in a reduced fluid velocity profile up to a certain value. After this point, the velocity profile is nearly flat in the domain, but an enhanced temperature profile is observed within the pipe. Furthermore, the maximum temperature increases as the heat source intensity increases. Additionally, higher values of the heat source lead to a point of inflection and flow separation in the velocity profile. The velocity profile becomes smooth as well as flat when elevated drag force values are exerted in the medium.
  Keywords: heat source effect; porous medium; magnetic effect; spectral collocation method.
  DOI: 10.1504/IJMMNO.2025.10072273
   
  
• Sequential quadratic programming-based economic optimisation of an MAP/PH/1 queueing system with negative arrivals and unreliable repairers  
  by Sakshi Pakhrot, D.C. Sharma 
  Abstract: This paper studies an MAP/PH/1 queueing system with negative arrivals, unreliable repairers addressing the challenges posed by repair failures through the analysis of two models. In model 1, a failed repair leads to the removal of all positive arrivals from the system, while in model 2, a standby server is activated to ensure service continuity. The study compares the key performance measures (derived using matrix-analytic method) and economic functions of both models. We have also determined the optimum values of the profit functions for both models using sequential quadratic programming (SQP). The results indicate that model 2 leads to lower loss of positive arrivals and demonstrates greater economic efficiency compared to model 1.
  Keywords: negative arrivals; unreliable repairs; Markovian arrivals; phase-type service; matrix-analytic method; economic optimisation.
  DOI: 10.1504/IJMMNO.2025.10072275
   
  
• Simulating water infiltration from a strip source with radial basis functions methods  
  by Fatima-Ezzahra Sadik, Mohamed Sadik, El Hassan Ben-Ahmed 
  Abstract: Richards’ equation governs water infiltration in unsaturated soils but poses numerical challenges due to its nonlinearity and soil heterogeneity. This study investigates two meshless numerical methods the radial basis function partition of unity method with QR factorisation (RBF-PU-QR) and the radial basis function-generated finite-difference method with Gaussian radial basis functions (RBF-GA) to solve bidimensional infiltration problems under a strip source. RBF-PU-QR improves efficiency and stability through localised approximations and QR factorisation, while RBF-GA enhances accuracy via Gaussian kernels and finite-difference stencils. Numerical experiments on homogeneous and heterogeneous soil domains show that both methods accurately capture infiltration dynamics, with relative errors below 1% and 2%, respectively, with refined discretisation while maintaining reasonable execution times. These results highlight the stability, accuracy, and adaptability of RBF-based methods for simulating nonlinear flow in hydrological and environmental applications.
  Keywords: Richards’ equation; water infiltration; strip source; radial basis functions; meshless methods; hydrological modelling.
  DOI: 10.1504/IJMMNO.2025.10072289
   
  
• A note on backward error and condition number of polynomial two-parameter eigenvalue problems  
  by Bharati Borgohain, Niranjan Bora 
  Abstract: Study of eigenvalue problems associated with matrix polynomials with single or multiple parameters appears in many practical applications. Polynomial two-parameter eigenvalue problem (PTEP) is a special type of such problems, which consists of a system of two bivariate matrix polynomials with two spectral parameters. The numerical study of polynomial eigenvalue problem is an emerging area of research in recent times and sustainable progress has been made in the areas of numerical algorithms, sensitivity and backward error analysis. To know the error in a computed solution of eigenpairs, it is very much essential to analyse the backward errors and condition numbers of the problem. However, for PTEP of grade k, this analysis becomes more complex, than in the single-parameter case due to the interaction between the two parameters. In this paper, we consider the PTEP of grade k and provided new estimates of the normwise backward error and condition numbers.
  Keywords: backward error; condition number; Kronecker product; polynomial two-parameter eigenvalue problem; linear two-parameter eigenvalue problem.
  DOI: 10.1504/IJMMNO.2025.10072394
   
  
• A comparative analysis of autonomous and fuzzy non-autonomous SIQR models for infectious disease dynamics  
  by H.A. Bhavithra, S. Sindu Devi 
  Abstract: This study presents a comparative analysis of the classical autonomous SIQR model and a fuzzy non-autonomous SIQR model to simulate infectious disease dynamics under uncertainty. The autonomous model uses fixed parameter, while the fuzzy model incorporates time varying and fuzzy logic-based parameters to capture real world variability. The basic reproduction number is derived for both the models; however, the fuzzy model yields the range of values using membership function for transmission and recovery rates. Sensitivity analysis reveals the fuzzy model is more responsive to uncertainty, with up to 35% fluctuations in outcomes compare to less than 10% in the autonomous model. Incorporating fuzzy viral load results in more nuanced bifurcation patterns and adaptive control strategies. A collocation method is used for numerical simulation over 30 days, showing rapid convergence to disease free state. These findings highlight the fuzzy model potential for informing public strategies, especially during emerging outbreaks with uncertain data.
  Keywords: SIQR model; fuzzy logic; non-autonomous system; bifurcation analysis; fuzzy membership function; epidemic simulation.
  DOI: 10.1504/IJMMNO.2026.10072880
   
  
• Analysis of the impact of the normalisation technique in the CODAS method on supplier selection  
  by Dariusz Kacprzak 
  Abstract: Multi-criteria decision-making methods are applied to various fields of human activity, including the problems of supplier selection A key step in most of these methods is the choice of the technique used to normalise the decision matrix, i.e. the transformation of input data expressed in different units into dimensionless and comparable numerical values This paper analyses the effect of the normalisation technique used on the final values and rankings of alternatives in the combinative distance-based assessment method in a lumber supplier selection problem For this purpose, 12 normalisation techniques are used, each consisting of two formulas applied separately to the benefit-type and cost-type criteria To evaluate these normalisation techniques, a novel use of Hellwig's taxonomic method is proposed, which is then compared with popular measures based on Pearson's correlation coefficient and Spearman's rank correlation coefficient The results obtained confirm the validity of using the linear normalisation maximum-based method in the combinative distance-based assessment method.
  Keywords: CODAS method; Hellwig's taxonomic method; HTM; normalisation technique; objective criteria weights; supplier selection problem.
  DOI: 10.1504/IJMMNO.2026.10073007
   
  
• Mathematical and numerical modelling of coupled heat and moisture diffusions during infrared drying of a potato slice  
  by Biharilal Tudu, Nilkanta Barman, Himadri Chattopadhyay, Sudip Simlandi, Sushovan Chatterjee 
  Abstract: This work presents a mathematical model and solves it numerically to investigate the diffusion of heat and moisture during drying of a potato slice in the presence of infrared rays. The energy and species (i.e., the moisture content) conservation equations are considered here to model the drying process. The energy equation of the model includes a suitable volumetric heat source to represent the infrared rays to heat the potato slice and evaporate the moisture. The distribution of temperature and moisture content within the potato slice is predicted numerically and validated with published experimental data. With a good agreement, the simulation is extended further for parametric studies. It is found that the evaporation rate increases initially with time, and then it remains almost constant. It increases with the square of the infrared temperature. The heat and moisture transfer coefficients are then predicted under different infrared temperatures. Finally, the correlations as a function of the infrared temperature and processing time are developed to describe the drying process. A correlation for the drying time of the potato slice under different infrared temperatures is also presented.
  Keywords: potato slice; drying; infrared rays; modelling; transport phenomena.
  DOI: 10.1504/IJMMNO.2025.10073057
   
  

Special Issue on: Modelling and Optimisation of Power Electronics and Grid Connected Systems for xEV Applications

• Hardware implementation of modular hybrid power generation system architecture with sensor less controller for battery storage applications  
  by Narendra Kumar Muthukuri  
  Abstract: The increasing demand for sustainable and efficient energy systems has led to the development of advanced hybrid power generation (HPG) architectures that integrate renewable sources with battery energy storage. This paper presents a real-time implementation of a modular HPG system combining photovoltaic (PV) energy and a battery energy storage system (BESS), optimised through a high-gain DC-DC converter and a 15-level packed U cell (15PUC) multilevel inverter. A novel sensorless proportional-resonant (SLPR) controller is employed to enhance system stability, reduce harmonic distortion, and ensure compliance with IEEE 519-2014 standards. The proposed system efficiently manages energy flow between PV modules, BESS, and the inverter, enabling reliable standalone and off-grid power delivery. The high-gain converter boosts PV voltage to levels suitable for medium-power applications, while the 15PUC inverter delivers high-quality AC output with reduced switching stress. The SLPR controller ensures dynamic voltage regulation and harmonic mitigation, making the system ideal for residential and commercial energy systems. Simulation and experimental results validate the system’s performance under linear and nonlinear load conditions, demonstrating its potential as a robust and scalable solution for modern energy infrastructure.
  Keywords: MLI; PUC; HG high gain; sensorless proportional resonant; total harmonic distortion; hybrid power generation; HPG; battery storage systems.
  DOI: 10.1504/IJMMNO.2026.10072336
   
  
• Advanced cell-to-cell equalisation strategy for series connected Li-ion batteries in xEV applications  
  by Sridivya Vattem, Srinivasa Rao Gorantla, N. Bharath Kumar  
  Abstract: Lithium-ion batteries are widely used in energy storage systems for electric vehicles (EVs) and renewable applications due to their high energy density and long lifespan However, cell imbalance in battery packs leads to non-uniform states of charge (SoC), degrading performance, reducing cycle life, and posing safety risks such as thermal runaway Traditional passive balancing dissipates excess energy as heat, while active balancing improves efficiency but increases cost and complexity This paper proposes a novel interleaved flyback converter (IFBC) topology for active cell balancing, enabling efficient energy transfer and minimizing heat dissipation with reduced system complexity. A 48V battery pack with 12 series-connected cells using IFBC was developed and tested under charging, discharging, and normal modes. The system maintains a SoC difference below 2% for optimal balancing, achieving balance in 172.5, 352.3, and 238.2 seconds, respectively, across the three modes, demonstrating its effectiveness for practical battery management applications.
  Keywords: active cell balancing; ACB; lithium-ion battery; interleaved flyback converter; IFBC; state of charge; SoC; battery management system; BMS; electric vehicles.
  DOI: 10.1504/IJMMNO.2026.10072339
   
  
• Mathematical modelling and optimisation of electric vehicle battery management using the evolved bat algorithm in grid-connected systems  
  by Batchu Veena Vani, Dharavath Kishan 
  Abstract: The growing need to reduce greenhouse gas emissions and fossil fuel dependence is accelerating interest in electric vehicles (EVs). However, widespread EV adoption faces challenges like prolonged charging times, limited infrastructure, battery degradation, and grid stress. Battery swapping stations (BSS) offer a promising solution to reduce wait times and promote efficient battery usage. This paper proposes an enhanced battery swapping and charging mechanism for EVs using the evolved bat algorithm (EBA), which improves upon the original bat algorithm. The proposed system efficiently schedules battery swaps and charging processes, minimising downtime and optimising energy management in real-time operations. Experimental results demonstrate significant improvements in operational performance, reduced waiting times, and lower computational costs, highlighting the EBA’s potential for revolutionising EV battery management systems.
  Keywords: evolved bat algorithm; EBA; battery charging; battery swapping; electric vehicles.
  DOI: 10.1504/IJMMNO.2026.10072396
   
  
• New energy vehicle strategy for electric vehicle adoption in Asia for sustainable transportation  
  by Rajanand Patnaik Narasipuram, Bindu Vadlamudi, Amit Singh Tandon 
  Abstract: This study presents a comprehensive analysis of the new energy vehicle (EV) market in Asia, focusing on hybrid electric vehicles (HEV), plug-in hybrid electric vehicles (PHEV), battery electric vehicles (BEV), and fuel cell electric vehicles (FCEV). High battery costs are identified as a major barrier to adoption. The research emphasises the strategic placement of solar EV charging stations (SEVCS) to address traffic and infrastructure challenges. Mathematical models are used to predict adoption rates, considering factors such as car dimensions, battery warranty, lifespan, and charging infrastructure. The study also evaluates the impact of economic and informational policies, highlighting the importance of collaborative implementation. Standards for EV charging in Asia follow MS IEC 61851 and SAE J1772. The findings offer insights for policymakers to reduce costs, improve infrastructure, and raise consumer awareness, ultimately promoting sustainable transportation and better air quality across the region.
  Keywords: new energy vehicle; NEV; hybrid electric vehicle; HEV; plug-in hybrid electric vehicle; PHEV; battery electric vehicle; BEV; fuel cell electric vehicle; FCEV.
  DOI: 10.1504/IJMMNO.2026.10072603
   
  
• Optimising capacitated EV routing with quantum evolutionary algorithms and federated reinforcement learning  
  by K. Sarangam , Dharani Kumar Chowdary Mirappalli, K. Raghava Rao 
  Abstract: The capacitated electric vehicle routing problem (CEVRP) involves complex interdependencies between dynamic charging and route optimisation. Traditional metaheuristics like genetic algorithms and ant colony optimisation often underperform in large-scale, uncertain EV logistics. This paper presents a quantum-inspired hybrid evolutionary framework (QHIEF) that integrates quantum-inspired evolutionary algorithms (QIEA) with federated reinforcement learning (FRL) for online learning of routing and charging strategies. The problem is modelled as a mixed-integer nonlinear program (MINLP) with stochastic energy consumption and multiple-objective cost minimisation. A refined quantum-inspired differential evolution (QIDE) algorithm enhances route and charging decisions via quantum superposition and adaptive mutation. FRL-based demand forecasting supports real-time vehicle-to-grid (V2G) collaboration. Evaluations on large-scale datasets show a 7.6% reduction in travel distance, 21.3% increase in computational efficiency, and improved convergence over methods like DPCA, CBACO, and SIGALNS, highlighting the frameworks potential for scalable, efficient EV logistics.
  Keywords: quantum-inspired evolutionary algorithm; QIEA; federated learning-based optimisation; capacitated electric vehicle routing problem; CEVRP; grid-connected xEV systems; multi-objective optimisation for power electronics.
  DOI: 10.1504/IJMMNO.2026.10072654
   
  
• Modelling and optimisation of modified non-isolated DC-DC converters using average current mode controller for fuel cell electric vehicles  
  by Chintalapudi K. Krishna, Attuluri R. Vijay Babu 
  Abstract: Conventional proportional-integral (PI) controllers are commonly used in DC-DC converters for fuel cell-powered xEV systems to regulate voltage; however, they exhibit limitations in dynamic performance, particularly under variable load and fluctuating fuel cell outputs, leading to voltage deviations and higher ripple. To address these challenges, this study proposes the implementation of an average current mode (ACM) controller in a single-switch non-isolated DC-DC boost converter. The ACM controller operates by regulating the average inductor current, offering faster transient response, better load regulation, and enhanced stability compared to traditional PI control. Key features of the proposed method include precise voltage tracking, low output ripple, and robustness against input variations, making it highly suitable for real-world xEV applications. Simulation results validate the effectiveness of the ACM approach, maintaining output voltage within 200 V ± 1 V during load changes from 1.25 A to 2.5 A, while the PI controller shows deviations up to ±3 V. This comparative analysis underscores the ACM controllers superiority in ensuring efficient, stable, and high-quality power delivery in fuel cell-based xEV applications.
  Keywords: fuel cell; xEV; voltage regulation; PI controller; ACM controller; dynamic response; ripple reduction.
  DOI: 10.1504/IJMMNO.2026.10072882
   
  
• Advanced control strategies for modelling and optimisation of hybrid microgrid for xEV applications  
  by Ramanjaneya Reddy Nalavala, Bobbillapati Suneetha, Badugu Suresh, Mohammad Mahaboob Pasha 
  Abstract: This work investigates advanced control strategies for integrating renewable energy sources into hybrid microgrids with electric vehicle (EV) integration to enhance voltage quality and minimise harmonic distortion losses. Renewable energy-powered microgrids offer up to 25% improved energy reliability and efficiency but face challenges such as voltage fluctuations and harmonic distortions, which can reach distortion levels of 15% - 20% during peak variability. The inclusion of EVs introduces dynamic load profiles, further impacting grid stability. To address these issues, an adaptive neuro-fuzzy inference system (ANFIS) controller is employed, achieving a 30% reduction in voltage fluctuations and mitigating harmonic distortions by up to 40%. The ANFIS controller leverages neural network adaptability and fuzzy logic interpretability to manage nonlinear and uncertain behaviours in the system. Empirical analysis and simulations demonstrate the effectiveness of the proposed approach in optimising hybrid microgrid performance, supporting renewable energy and EV integration. The findings underscore the significant role of ANFIS controllers in improving grid stability and sustainability, enabling modern hybrid microgrids to achieve a more reliable and efficient energy infrastructure.
  Keywords: adaptive neuro-fuzzy inference system; ANFIS; electric vehicle; EV; harmonic distortion reduction; microgrids; renewable energy integration; voltage quality enhancement.
  DOI: 10.1504/IJMMNO.2026.10073026