Papers by Iranian journal of Numerical Analysis and Optimization
Ferdowsi University of Mashhad, 2025
This research explores a continuous-time mathematical model that outlines the transmission dynami... more This research explores a continuous-time mathematical model that outlines the transmission dynamics of the dengue virus across different regions, involving both human and mosquito hosts. We propose an optimal strategy that includes awareness campaigns, safety measures, and health interventions in dengue-endemic areas, with the goal of reducing transmission between individuals and mosquitoes, thus lowering human infections and eliminating the virus in mosquito populations. Utilizing the discrete-time *Corresponding author
Ferdowsi University of Mashhad, 2025
In the current study, we design a new computational method to solve a class of Liénard's equation... more In the current study, we design a new computational method to solve a class of Liénard's equations. This equation originates from advancements in radio and vacuum tube technology. To attain the proposed goal, we develop a method using a three-layer artificial neural network, consisting of an input layer, a hidden layer, and an output layer. We use the Morgan-Voyce even Fibonacci polynomials and sinh function as activation functions for the hidden layer and the output layer, respectively. Then, the neural network is trained using a classical optimization method. Finally, we analyze four examples using graphs and tables to demonstrate the accuracy and effectiveness of the numerical approach.
In the current study, we design a new computational method to solve a class of Liénard's equation... more In the current study, we design a new computational method to solve a class of Liénard's equations. This equation originates from advancements in radio and vacuum tube technology. To attain the proposed goal, we develop a method using a three-layer artificial neural network, consisting of an input layer, a hidden layer, and an output layer. We use the Morgan-Voyce even Fibonacci polynomials and sinh function as activation functions for the hidden layer and the output layer, respectively. Then, the neural network is trained using a classical optimization method. Finally, we analyze four examples using graphs and tables to demonstrate the accuracy and effectiveness of the numerical approach.
Ferdowsi University of Mashhad, 2025
In this study, we investigate the numerical exploration of the Peyrard-Bishop DNA (PBD) dynamic m... more In this study, we investigate the numerical exploration of the Peyrard-Bishop DNA (PBD) dynamic model. These solutions are responsible for analyzing the nonlinear interactions between the adjacent displacements of the DNA strand. To obtain these solutions, the authors present two highly
Ferdowsi University of Mashhad, 2025
Leishmania is an infectious disease that is difficult to control and has an impact on morbidity a... more Leishmania is an infectious disease that is difficult to control and has an impact on morbidity and mortality around the world. This study investigates the dynamics of cutaneous Leishmania and optimal control measures, particularly in regards to human immigration. Applying a mathematical model to evaluate the dynamics of human immigration and sand flies population. The human population is classified into four compartments: susceptible, exposed, infectious, and recovered. The sand fly population is divided into three categories: susceptible, exposed, and infectious. The
Ferdowsi University of Mashhad, 2025
We develop a fitted tension spline numerical scheme for singularly perturbed parabolic problems w... more We develop a fitted tension spline numerical scheme for singularly perturbed parabolic problems with a large temporal lag. A priori bounds and *Corresponding author
Ferdowsi University of Mashhad, 2025
We develop a fitted tension spline numerical scheme for singularly perturbed parabolic problems w... more We develop a fitted tension spline numerical scheme for singularly perturbed parabolic problems with a large temporal lag. A priori bounds and *Corresponding author
Ferdowsi University of Mashhad, 2025
This paper focuses on solving singularly perturbed parabolic equations of the convection-diffusio... more This paper focuses on solving singularly perturbed parabolic equations of the convection-diffusion type with a large negative spatial shift and an integral boundary condition. A higher-order uniformly convergent numerical approach is proposed that uses Crank-Nicolson and a hybrid finite difference approximation on a piece-wise uniform Shishkin mesh. Simpson's 1/3 integration rule is used to treat the integral boundary condition. The proposed method has been shown to achieve almost second-order uniform convergence. The computational results derived from the numerical *Corresponding author
Ferdowsi University of Mashhad, 2025
In this work, the stability results for a nonlinear mathematical model are derived, and the power... more In this work, the stability results for a nonlinear mathematical model are derived, and the power system is realized by utilizing fractional calculus theory. The fixed point theorem is used to establish sufficient conditions for the existence of a mild solution and the stability of a nonlinear impulsive fractional stochastic integro-differential equation with state-dependent delays with Mainardi's function in a Hilbert space. Numerical simulations are provided to validate the obtained theoretical results. The proposed *Corresponding author
Ferdowsi University of Mashhad, 2025
Particle swarm optimization (PSO) is a widely recognized bio-inspired algorithm for systematicall... more Particle swarm optimization (PSO) is a widely recognized bio-inspired algorithm for systematically exploring solution spaces and iteratively identifying optimal points. Through updating local and global best solutions, PSO effectively explores the search process, enabling the discovery of the most advantageous outcomes. This study proposes a novel Smith chartbased particle swarm optimization to solve convex and nonconvex multiobjective engineering problems by representing complex plane values in *Corresponding author
Ferdowsi University of Mashhad, 2025
Water pollution can have many adverse effects on the environment and human health. The study of t... more Water pollution can have many adverse effects on the environment and human health. The study of the transmission of water pollutants over a finite lifespan is carried out using an optimal control problem (OCP), with the system governed by ordinary differential equations. By utilizing the collocation approach, the OCP is transmuted to a nonlinear programming problem, and then the mountain Gazelle algorithm is applied to determine the optimal control and state solutions. A practical study demonstrates the effect of treatment on reducing water pollutants during a finite time.
Ferdowsi University of Mashhad, 2025
In this study, Allee type, single-species (prey), two-patch model with nonlinear harvesting rate,... more In this study, Allee type, single-species (prey), two-patch model with nonlinear harvesting rate, and species migration across two patches have been developed and analyzed. As we all know, the population of any species in an ecosystem is greatly dependent on the carrying capacity of the corresponding ecosystem; the main focus of our work is on how carrying capacity affects system dynamics in the presence and absence of randomness (deterministic and stochastic case, respectively). In the deterministic case,
The conjugate gradient (CG) method is an optimization technique known for its rapid convergence; ... more The conjugate gradient (CG) method is an optimization technique known for its rapid convergence; it has blossomed into significant developments *Corresponding author
Ferdowsi University of Mashhad, 2025
The main focus of this work is to develop and implement an efficient local discontinuous Galerkin... more The main focus of this work is to develop and implement an efficient local discontinuous Galerkin scheme for acquiring the numerical solution of the (1 + 1)-dimensional nonlinear Kolmogorov-Petrovskii-Piskunov equation. The proposed framework employs a local discontinuous Galerkin discretization technique in the spatial direction and a higher-order total variation diminishing Runge-Kutta scheme in the temporal direction. The L 2 stability of the local discontinuous Galerkin method, which is ensured by carefully selecting the interface numerical fluxes, is discussed in detail.
Ferdowsi University of Mashhad, 2025
This study presents the process of using extrapolation methods to solve the nonlinear Volterra-Fr... more This study presents the process of using extrapolation methods to solve the nonlinear Volterra-Fredholm integral equations of the second kind. To do this, by approximating the integral terms contained in equations by a quadrature rule, the nonlinear Volterra-Fredholm integral equations of the *Corresponding author
This study presents the process of using extrapolation methods to solve the nonlinear Volterra-Fr... more This study presents the process of using extrapolation methods to solve the nonlinear Volterra-Fredholm integral equations of the second kind. To do this, by approximating the integral terms contained in equations by a quadrature rule, the nonlinear Volterra-Fredholm integral equations of the *Corresponding author
Ferdowsi University of Mashhad, 2025
The recent outbreak of the COVID-19 disease has just appeared at the end of 2019 that has now bec... more The recent outbreak of the COVID-19 disease has just appeared at the end of 2019 that has now become a global pandemic. Analysis of mathematical models in the prediction and control of this pandemic helps to make the right decisions about vaccination, quarantine, and other control measures.
Ferdowsi University of Mashhad, 2025
The conjugate gradient method is one of the most important ideas in scientific computing. It is a... more The conjugate gradient method is one of the most important ideas in scientific computing. It is applied to solving linear systems of equations and nonlinear optimization problems. In this paper, based on a variant of the Hestenes-Stiefel (HS) method and Polak-Ribière-Polyak (PRP) method, two modified conjugate gradient methods (named MHS * and MPRP *) are presented and analyzed. The search direction of the presented methods fulfills the sufficient descent condition at each iteration. We establish the global convergence of the proposed algorithms under normal assumptions and strong Wolfe line search. Preliminary elementary numerical experiment results are presented, demonstrating the promise and the effective-*Corresponding author
Ferdowsi University of Mashhad, 2024
This study delves into the potential polynomial and rational wave solutions of the Kudryashov-Sin... more This study delves into the potential polynomial and rational wave solutions of the Kudryashov-Sinelshchikov equation. This equation has multiple applications including the modeling of propagation for nonlinear waves in various physical systems. Through detailed numerical simulations using the finite element approach, we present a set of accurate solitary and soliton solutions for this equation. To validate the effectiveness of our proposed method, we utilize a collocation finite element approach based on quintic B-spline functions. Error norms, including L 2 and L∞, are employed to assess the precision of our numerical solutions, ensuring their reliability and accuracy. Visual representations, such as graphs derived from tabulated data, offer valuable insights into the dynamic changes of the equation over time or in response to varying parameters. Furthermore, we compute conservation quantities of motion and investigate the stability of our numerical scheme using Von Neumann theory, providing a comprehensive analysis of the Kudryashov-Sinelshchikov equation and the robustness of our computational approach. The strong alignment between our analytical and numerical results underscores the efficacy of our methodology, which can be extended to tackle more complex nonlinear models with direct relevance to various fields of science and engineering.
Ferdowsi University of Mashhad, 2024
This study explores a continuous spatio-temporal mathematical model to illustrate the dynamics of... more This study explores a continuous spatio-temporal mathematical model to illustrate the dynamics of Monkeypox virus spread across various regions, considering both human and animal hosts. We propose a comprehensive
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Papers by Iranian journal of Numerical Analysis and Optimization