Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201A semi-analytical study on Hepatitis A virus transmission in Indonesia118912204804210.22067/ijnao.2026.97008.1804ENA.MaheswariDepartment of Mathematics, Velammal College of Engineering and Technology, Madurai,
Tamil Nadu, India.V.AnanthaswamyResearch Centre and PG, Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University),
Madurai, Tamil Nadu, India.0000-0002-2938-8745J.Anantha JothiResearch Centre and PG, Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University),
Madurai, Tamil Nadu, India.Journal Article20251215A mathematical layout that depicts the epidemiology of Hepatitis A (HA) in Indonesia is analysed in the present research. The framework's specific four compartments -Susceptible, Individuals, Treatment, and Recovered are resolved approximate analytically through the Laplace Adomian decomposition technique (LADM) and Taylor series method (TSM). For each of the four compartments, the approximate analytical answers are stated. The outcomes of multiple kinds of model parameters are demonstrated graphically. The numerical simulation (MATLAB) and our approximate analytical outcomes are contrasted and provided in the table. The approximate analytical outcomes and the numerical simulation fit each other precisely.https://ijnao.um.ac.ir/article_48042_6f67a4862f1c12f6e164ff38655538a2.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201Second-kind Chebyshev spectral Petrov-Galerkin scheme for solving the time-fractional Euler-Bernoulli beam equation122112384825010.22067/ijnao.2026.97767.1839ENYoussri HassanYoussriDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt.0000-0003-0403-8797Maha MuftahMuttardiMathematics and Actuarial Science Department, School of Science and Engineering, The
American University in Cairo, New Cairo 11835, Egypt.0000-0002-0637-2994Journal Article20260209This work introduces a novel Petrov-Galerkin spectral technique designed to investigate vibrational behavior in fourth-order time-fractional Euler--Bernoulli beams with pinned-pinned boundary conditions. A tailored basis comprising shifted second-kind Chebyshev polynomials is developed, which automatically fulfills homogeneous boundary constraints, thus lowering computational demands. By selecting test functions from the same Chebyshev family, the Petrov-Galerkin framework converts the fractional partial differential equation into a structured algebraic system that can be efficiently resolved through Gaussian elimination. The proposed scheme delivers exponential convergence for sufficiently smooth solutions, exhibits low numerical dispersion, and remains straightforward to implement even for high-order problems. Rigorous error estimates in both $L_\infty$ and $L_2$ norms ensure theoretical reliability. Computational tests, including a case lacking a closed-form exact solution, validate the precision and computational efficiency of the approach.https://ijnao.um.ac.ir/article_48250_5346b5c4f02edb816860d9ade175e863.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201Analysis and optimal control of a proliferating-quiescent Glioma model with combined therapy123912704806710.22067/ijnao.2026.97425.1826ENTawfikJaberLaboratory of fundamental mathematics and their application, Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, El Jadida, Morocco.OmarBalatifLaboratory of fundamental mathematics and their application, Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, El Jadida, Morocco.0000-0003-1887-5350Journal Article20260129Low-grade gliomas (LGGs) are slow-growing but infiltrative brain tumors characterized by long-term persistence and frequent progression. In this work, we develop and analyze a compartmental mathematical model describing LGG dynamics under combination therapy involving cytotoxic chemotherapy and targeted molecular treatment. The tumor population is structured into proliferating, quiescent, and damaged compartments, and therapeutic interventions are incorporated through bilinear control terms accounting for chemo-therapies. We first establish the well-posedness of the model by proving existence, uniqueness, positivity, and boundedness of solutions. The dynamics of untreated glioma growth are then analyzed, revealing that the tumor-free equilibrium is always unstable in the absence of therapy, leading to exponential tumor expansion. Under constant treatment regimens, we derive an explicit controlled reproduction number that governs tumor persistence or eradication. Using linearization and Lyapunov–LaSalle stability techniques, we establish necessary and sufficient conditions for both local and global asymptotic stability of the tumor-free state. Finally, we formulate an optimal control problem to identify treatment strategies that minimize tumor burden while limiting therapeutic toxicity. The existence of optimal controls is rigorously proven using classical results from optimal control theory. Our results provide analytical insight into the stabilizing role of combination therapy and offer a quantitative guidance for designing optimized treatment protocols for low-grade glioma.https://ijnao.um.ac.ir/article_48067_3fc2d2c3597b3e7b87c17651f98f6c22.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201Travelling wave patterns and bifurcation dynamics in a spatial predator–prey model127112944836710.22067/ijnao.2026.97551.1828ENSaddamHussainDepartment of Mathematics and Computing Technology, NIT Patna, India.0009-0000-2517-9316MoitriSenDepartment of Mathematics and Computing Technology, NIT Patna, India.Journal Article20260130We have studied a diffusive predator–prey model with nonlinear predator–prey interactions and prey dispersal. Using bifurcation analysis combined with numerical simulations, we reveal a rich variety of dynamical behaviors, including the stability of steady states, wave fronts, wave pulses, periodic and multi-periodic wave trains, and chaotic spatiotemporal patterns. The results show that diffusion and interaction strength play a critical role in shaping the travelling-wave dynamics through saddle–node, Hopf, and period–doubling bifurcations. In particular, increasing diffusion can destabilize steady states and induce oscillatory dynamics, ultimately leading to chaotic population fluctuations. These findings provide ecological insight into how spatial dispersal and nonlinear interactions shape complex population patterns in predator–prey systems.https://ijnao.um.ac.ir/article_48367_07882514141f3f7512e11dfd1757d2d3.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201Practical early stopping for adaptive barrier SGD: balancing stochastic speed with validation accuracy129513184794610.22067/ijnao.2026.96710.1788ENAbdelouakilFillaliFaculty of Mathematics and Informatics, Department of Mathematics, University Mohamed El Bachir El Ibrahimi of Bordj Bou-Arreridj,Algeria.0009-0002-8907-4876SmailAddouneFaculty of Mathematics and Informatics, Department of Mathematics, University Mohamed El Bachir El Ibrahimi of Bordj Bou-Arreridj,Algeria.RebihaZeghdaneFaculty of Mathematics and Informatics, Department of Mathematics, University Mohamed El Bachir El Ibrahimi of Bordj Bou-Arreridj,Algeria.Journal Article20251126Stochastic Gradient Descent (SGD) algorithms based on adaptive barrier functions are highly efficient for large-scale constrained optimization. However, their inherent stochastic nature leads to the critical ”last- iterate problem”, where update noise causes significant oscillations, making reliance on the final solution a high-stakes gamble. To address this instability, we introduce the Early-Stopped Barrier SGD (EB-SGD) algorithm, a practical approach that replaces reliance on the noisy last iterate with a robust ”best-iterate tracking” mechanism. Our method employs periodic validation, where the cheap stochastic process is temporarily halted to compute a high-quality, deterministic ”Validation Score.” This score is defined as a combination of the full-batch objective function and a large penalty for constraint violation. We maintain the iterate that achieves the best score recorded so far and utilize a ”patience”-based stopping criterion to filter out minor stochastic oscillations and halt the algorithm only upon persistent stagnation. This strategy introduces a deliberate computational trade-off: exchanging many inexpensive stochastic steps for fewer, more expensive validation steps. We prove theoretically that the sequence of best iterates returned by EB-SGD converges almost surely to the unique optimal solution. Furthermore, our numerical experiments confirm the practical superiority of this approach, demonstrating significantly reduced variance (higher stability) and finding a final solution that is substantially more accurate than the baseline last-iterate method.https://ijnao.um.ac.ir/article_47946_26099adf9fe6be27c19d1a0fb68d7985.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201A novel collocation-based numerical method for higher-order linear ODE systems with pharmacokinetic applications131913404845510.22067/ijnao.2026.97725.1837ENFatmaKaciDepartment of Mathematics, Faculty of Exact Sciences, Mohamed Khider University, Biskra, Algeria.Journal Article20260206This paper introduces a collocation method founded on the independence polynomial of the path graph to solve systems of linear differential equations subject to mixed conditions. The approach converts the original differential system and its associated conditions into an equivalent matrix representation, resulting in a linear algebraic system whose unknowns are the independence coefficients. Several test problems are conducted to assess the numerical efficiency and accuracy of the method. As a practical application, the technique is applied to the three-compartment pharmacokinetic model, illustrating its robustness, numerical stability, and computational simplicity. The results demonstrate the proposed method’s effectiveness and reliability in solving complex systems of differential equations.https://ijnao.um.ac.ir/article_48455_e355819c0931a90b594aeb8d6a73587f.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201Conformable fractional power series method for solving Fisher-Kolmogorov-Petrovskii-Piskunov equation134113654795010.22067/ijnao.2026.96531.1779END. L.SutharDepartment of Mathematics, Wollo University, Dessie, Ethiopia.FasilDesalewDepartment of Mathematics, Wollo University, Dessie, Ethiopia.MulualemAychluhDepartment of Mathematics, Samara University, Samara, Ethiopia.0000-0002-5295-1559GizachewTiriteDepartment of Mathematics, Debre Tabor University, Debre Tabor, Ethiopia.0009-0002-0756-0361Journal Article20251118This work discusses the application of the conformable fractional power series method to approximate the nonlinear time-fractional Fisher–Kolmogorov–Petrovskii–Piskunov equation, which is used to model tumour growth and invasion. By employing the conformable derivative, the method converts the fractional equation into a recursive series expansion, resulting in accurate semi-analytical approximations. Three numerical examples involving various nonlinear powers have been solved. Analyses of convergence and error for the series solution have been conducted. The results show a remarkable agreement with both the exact solutions and existing numerical results, with very small absolute errors observed in all test cases. The results show a remarkable agreement with both the exact solutions and existing numerical results, with very small absolute errors observed in all test examples.https://ijnao.um.ac.ir/article_47950_189627e6dfdb79c621a10584770d0427.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201Impact of lifestyle interventions and adequate medical infrastructure on diabetes prevention: Dynamics analysis and optimal control136614004818610.22067/ijnao.2026.97704.1834ENManashKalitaDepartment of Mathematics, Lakhimpur Girls’ College, Lakhimpur 787031, Assam, India.Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India.ZenithMondalDepartment of Mathematics, Rabindranath Thakur Vishwavidyalaya, Hojai 782436, Assam, India.BarlinBhuyanDepartment of Mathematics, Mahapurusha Srimanta Sankaradeva Viswavidyalaya, Nagaon 782001, Assam, India.Bhagya JyotiNathDepartment of Mathematics, Rabindranath Thakur Vishwavidyalaya, Hojai 782436, Assam, India.0000-0002-4001-4592Hemanta KumarSarmahDepartment of Mathematics, Gauhati University, Guwahati 781014, Assam, India.Journal Article20260205Diabetes mellitus is a chronic metabolic disorder that affects the ability to regulate blood glucose levels in the human body. In recent decades, the rapid increase in the number of people living with diabetes around the world has made it one of the most pressing public health concerns and places a growing burden on healthcare systems. In this study, we formulate and analyze a non-linear mathematical model to study the effect of lifestyle intervention and proper medical infrastructure on diabetes prevention. We study the basic properties of the model system, like the existence, non-negativity, and boundedness of solutions. Further, a non-trivial equilibrium point for the model system has been found, and local and global stability of the equilibrium point are established. Additionally, we propose an optimal control problem by introducing two control variables that prevent healthy people from becoming pre-diabetic due to a bad lifestyle through spreading awareness about lifestyle intervention and clinical intervention to enhance the treatment rate of the diabetic population with complications. The optimal control problem is further solved to reduce the burden of diabetics with and without complications. Finally, our findings suggest that lifestyle intervention aimed at raising awareness among the healthy population about irregular lifestyles, together with adequate medical infrastructure to improve treatment rates among diabetic individuals with complications, can substantially ease the growing strain imposed by diabetes on healthcare systems.https://ijnao.um.ac.ir/article_48186_c2102c66aa81e5c07f72cd88e46d091d.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201Mathematical modeling and control strategies for meningitis transmission140114314850810.22067/ijnao.2026.96797.1789ENMohamedBaroudiLaboratory of Advanced Research in Industrial and Logistic Engineering (LARILE),
Applied Mathematics Team, Department of Mathematics and Computer Science, ENSEM,
Hassan II University of Casablanca, Morocco.0009-0006-8669-5764BenyounesBettiouiCentre R´egional des M´etiers de l’´Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco.MohamedBelamLaboratory of Advanced Research in Industrial and Logistic Engineering (LARILE),
Applied Mathematics Team, Department of Mathematics and Computer Science, ENSEM,
Hassan II University of Casablanca, Morocco.AbderrahimLabzaiLaboratory of Analysis Modeling and Simulation, Department of Mathematics and
Computer Science, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca,
Morocco.Journal Article20251202Meningitis is one of the world’s most alarming infectious diseases, characterized by rapid progression, high fatality, and severe long-term complications. Despite advances in vaccination and surveillance, recurrent epidemics—especially across Africa’s “meningitis belt”—continue to threaten millions. This study introduces a novel compartmental model, SEAIV HRQ, integrating both medical and behavioral aspects of meningitis dynamics. The model divides the population into eight classes, incorporating vaccination and voluntary quarantine to reflect realistic public health conditions. Three time-dependent controls are applied to reduce transmission from asymptomatic and symptomatic individuals and to enhance awareness and treatment adherence. Using Pontryagin’s Maximum Principle, we determine optimal strategies that minimize infection prevalence, hospitalization, and intervention costs. Numerical simulations show that combined preventive, treatment, and awareness measures substantially reduce infection peaks and accelerate recovery. This framework extends classical models and supports the WHO’s “Defeating Meningitis by 2030” roadmap, offering practical insights for designing cost-effective and sustainable control strategies in resource-limited health systems.https://ijnao.um.ac.ir/article_48508_f473cce8e1fe128830d36a2c5216b213.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201Design of a multi-stage hybrid optimizer combining Bayesian and evolutionary algorithms for modeling and optimizing seizure-related information in EEG signals143214634826410.22067/ijnao.2026.94741.1697ENMaryamKhansariFaculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.HoomanAfshariradFaculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article20250803The prediction of epileptic seizures from EEG signal analysis is modeled as a complex, high-dimensional, multi-objective optimization problem. In this study, we propose and design a novel multi-stage hybrid optimizer that integrates Bayesian optimization with a family of evolutionary and metaheuristic algorithms, including Genetic Algorithm (GA), Evolutionary Programming (EP), Evolution Strategies (ES), Ant Colony Optimization (ACO), Artificial Bee Colony (ABC), and Harmony Search (HS).This optimizer is structured to operate across sequential stages of optimization, where each stage is designed to progressively refine the solution space by selecting the optimal subset of EEG channels and time blocks related to the preictal phase. The mathematical model aims to maximize the posterior probability of seizure occurrence while minimizing the temporal distance to the actual seizure, thus formulating a well-defined trade-off in the objective space. Unlike traditional methods, the proposed hybrid framework models and controls the optimization trajectory by combining the global exploration capability of evolutionary algorithms with the adaptive search of Bayesian optimization. Experimental results demonstrate that the optimizer successfully converges toward high-informational regions of EEG data that occur early in the preictal phase. A detailed performance comparison and sensitivity analysis further validate the effectiveness and robustness of the proposed approach, offering insights into the design of more generalizable hybrid optimizers for complex modeling tasks.https://ijnao.um.ac.ir/article_48264_e11a3aa5a5d08443e5532d304e851f39.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201Coupled fixed points for a class of non-cyclic contractions in uniformly convex Banach spaces with error estimates146414834832710.22067/ijnao.2026.98129.1861ENAkramSafari-HafshejaniDepartment of Pure Mathematics, Payame Noor University (PNU), P. O. Box: 19395- 3697, Tehran, Iran.0000-0002-5955-2470KhadijeAmiriDepartment of Pure Mathematics, Payame Noor University (PNU), P. O. Box: 19395- 3697, Tehran, Iran.Journal Article20260311In this paper, we introduce a non-cyclic contraction pair of an ordered pair of mappings. We then deduce the existence and uniqueness of coupled fixed points by associating a non-cyclic contraction with them. In addition, we obtain both a priori and a posteriori error estimates for these points in uniformly convex Banach spaces. The main result is illustrated with an example, and as an application, a cyclic version of the main theorem is derived. In addition, we obtain both a priori and a posteriori error estimates for these points in uniformly convex Banach spaces. The main result is illustrated with an example, and as an application, a cyclic version of the main theorem is derived.https://ijnao.um.ac.ir/article_48327_90e28e9640702d0120b0fa38f61c4c42.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201A multi-layer SEIRS-V network epidemic model for IoT malware propagation with heterogeneous device types and patch dynamics148415174844910.22067/ijnao.2026.97856.1846ENAliakbarTajari SiahmarzkoohDepartment of Computer Science, Golestan University, Gorgan, IranJournal Article20260214The Internet of Things (IoT) ecosystem comprises billions of heterogeneous devices with diverse hardware architectures, operating systems, vulnerability profiles, and patch management capabilities, creating a complex and dynamic attack surface for malware propagation. This paper develops a comprehensive multi-layer network epidemic model for characterizing malware spread in heterogeneous IoT networks. The proposed framework integrates three key dimensions: (1) a Susceptible-Exposed-Infected-Recovered-Susceptible with Vaccination (SEIRS-V) compartmental structure capturing device-level infection states and patching status, (2) a multi-layer network topology distinguishing between physical proximity, logical connectivity, and protocolbased communication graphs, and (3) device-type heterogeneity with class-specific parameters for vulnerability, infectiousness, and recovery rates. The hybrid formulation yields a system of coupled differential equations that admits analytical expressions for the basic reproduction number R0, type-specific epidemic thresholds, and equilibrium prevalence. Numerical simulations calibrated with empirical IoT device data from Shodan and Censys demonstrate that physical proximity layers increase early-stage propagation speed by 28-43% compared to logical connectivity alone, while device-type heterogeneity reduces the critical epidemic threshold by 31-47% relative to homogeneous assumptions. The model provides security analysts with quantitative tools for identifying critical infection pathways, prioritizing device classes for patching, and evaluating network segmentation strategies.https://ijnao.um.ac.ir/article_48449_babd046c02ed033d6633ccb5bc12e57e.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201A collocation framework for numerical reconstruction of the source function in a two-term fractional diffusion problem151815494837610.22067/ijnao.2026.97820.1844ENSaharJalalianDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.AfshinBabaeiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.0000-0002-6980-9786MortezaGachpazanDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.0000-0001-5662-0207Journal Article20260213This study develops a new spectral collocation strategy to reconstruct an unknown source term appearing in a two-term time-fractional diffusion model equipped with nonlocal boundary constraints. As obtaining an exact solution to such problems is generally intractable, a collocation strategy based on Legendre polynomials and Chebyshev nodes is employed to construct the numerical approximation. By projecting the fractional-order operators onto a bivariate polynomial basis, the original inverse problem is transformed into a system of linear algebraic equations. The solvability of the resulting system is investigated via the properties of the associated collocation matrix incorporating the fractional dynamics and nonlocal boundary conditions. Moreover, convergence analysis and rigorous error. Numerical trials are presented to demonstrate the reliability, precision, and computational efficiency of the proposed procedure.https://ijnao.um.ac.ir/article_48376_d37a453951288d88fbd05288ab3c11cd.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201Fractional order Chelyshkov wavelet for solving variable coefficients Caputo time-fractional convection-diffusion equation155015904853310.22067/ijnao.2026.97711.1835ENSufiaSabirDepartment of Mathematics and Computing Technology, National Institute of Technology Patna, Patna, 800005, Bihar, India.AyazAhmadDepartment of Mathematics and Computing Technology, National Institute of Technology Patna, Patna, 800005, Bihar, India.Journal Article20260205Convection-diffusion equations are widely used to describe transport processes and arise in numerous scientific and engineering applications, including heat transfer, contaminant transport in porous media, groundwater flow, chemical reactions, and biological systems. However, many real-world transport phenomena exhibit memory properties that classical convection-diffusion equations cannot adequately represent. To address such nonlocal temporal effects, time-fractional convection-diffusion equations have been introduced, in which fractional derivatives provide a realistic description of anomalous diffusion. This work proposes a novel wavelet-based numerical method for solving a variable-coefficient Caputo time-fractional convection-diffusion equation using fractional-order Chelyshkov wavelets. The method constructs fractional Chelyshkov wavelets from fractional Chelyshkov polynomials and derives corresponding fractional operational matrices. The proposed wavelet basis functions, together with an operational matrix formulation, transform the time-fractional convection-diffusion equation into a system of algebraic equations. The stability, convergence, and error estimate are established. To demonstrate the effectiveness and precision of the proposed method, several numerical examples are provided. CPU time and memory usage are reported for different numbers of basis functions. The numerical results indicate that the fractional Chelyshkov wavelets provide an efficient representation of smooth solutions, achieving high accuracy with a relatively small number of basis functions.https://ijnao.um.ac.ir/article_48533_06a551ad447cbd2ccc4820f966cc070e.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697716Issue 420261201Queueing analysis of a VoIP call center under retrial policy with re-service, server maintenance, and service disruptions159116214803310.22067/ijnao.2026.96253.1768ENPreenaR.Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore, Tamil Nadu, India.0009-0001-2481-8187SumithaD.Department of Science and Humanities, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore, Tamil Nadu, India.0000-0001-8105-6521Journal Article20251030This paper develops a retrial queueing framework for a Voice over Internet Protocol (VoIP) call center server with two obligatory service phases. Incoming voice packets arrive according to the Poisson process. The model captures caller behavior involving potential re-service requests based on satisfaction after the first phase, introducing dynamic retrial effects. It integrates operational uncertainties such as service disruptions due to malware attacks and immediate repair processes. Additionally, server maintenance activities and post maintenance buffer searches are integrated to reflect realistic system operations. The supplementary variable technique is employed to derive steady state solutions for performance evaluation. Numerical analysis highlights the influence of key parameters on system performance. To enhance the study, cost optimization is performed using the Particle Swarm Optimization (PSO) technique, offering effective strategies to balance service quality and operational cost.https://ijnao.um.ac.ir/article_48033_8b716c818254eda3b897eb0ba7c5999f.pdf