Papers by Iranian journal of Numerical Analysis and Optimization
Ferdowsi University of Mashhad, 2024
The Barzilai-Borwein method offers efficient step sizes for large-scale unconstrained optimizatio... more The Barzilai-Borwein method offers efficient step sizes for large-scale unconstrained optimization problems. However, it may not guarantee global convergence for nonquadratic objective functions. Simulated annealingbased on Barzilai-Borwein (SABB) method addresses this issue by incorporating a simulated annealing rule. This work proposes a novel step-size strategy for the SABB method, referred to as the SABBm method. Furthermore, we introduce two stabilized variants: SABBstab and SABBmstab. SABBstab combines a simulated annealing rule with a stabilization step to ensure convergence. SABBmstab builds upon SABBstab,
Ferdowsi University of Mashhad, 2024
This paper aims to extend a Krylov subspace technique based on an incomplete orthogonalization of... more This paper aims to extend a Krylov subspace technique based on an incomplete orthogonalization of Krylov tensors (as a multidimensional extension of the common Krylov vectors) to solve generalized Sylvester tensor equations via the Einstein product. First, we obtain the tensor form of the quasi-GMRES method, and then we lead to the direct variant of the proposed algorithm. This approach has the great advantage that it uses previous data in each iteration and has a low computational cost. Moreover, an upper bound for the residual norm of the approximate solution is found. Finally, several experimental problems are given to show the acceptable accuracy and efficiency of the presented method.
Ferdowsi University of Mashhad, 2024
The goal of this study is to use our suggested generalized Legendre wavelet method to solve delay... more The goal of this study is to use our suggested generalized Legendre wavelet method to solve delay and equations of neutral differential form with proportionate delays of different orders. Delay differential equations have some application in the mathematical and physical modelling of real-world problems such as human body control and multibody control systems, electric circuits, dynamical behavior of a system in fluid mechanics, chemical engineering, infectious diseases, bacteriophage infection's spread, population dynamics, epidemiology, physiology, immunology, and neural networks.
Ferdowsi University of Mashhad, 2024
The presented work introduces a new class of nonlinear optimal control problems in two dimensions... more The presented work introduces a new class of nonlinear optimal control problems in two dimensions whose constraints are nonlinear Ginzburg−Landau equations with fractal−fractional (FF) derivatives. To acquire their approximate solutions, a computational strategy is expressed using the FF derivative in the Atangana−Riemann−Liouville
Ferdowsi University of Mashhad, 2024
This research paper deals with the numerical method for the solution of high-order Fredholm integ... more This research paper deals with the numerical method for the solution of high-order Fredholm integro-differential difference equations using Legendre polynomials. We obtain the integral form of the problem, which is transformed into a system of algebraic equations using the collocation method. We then solve the algebraic equation using Newton's method. We establish the uniqueness and convergence of the solution. Numerical problems are considered to test the efficiency of the method, which shows that the method competes favorably with the existing methods and, in some cases, approximates the exact solution.
Ferdowsi University of Mashhad, 2024
In this paper, we explore the numerical analysis of the microscale heat equation. We present the ... more In this paper, we explore the numerical analysis of the microscale heat equation. We present the characteristics of numerical solutions obtained through both semi-and fully-discrete linear finite element methods. We establish a priori estimates and error bounds for both semi-discrete and fully-discrete finite element approximations. Additionally, the existence and uniqueness of the semi-discrete and fully-discrete finite element approximations have been confirmed. The study explores error bounds in various spaces, comparing the semi-discrete to the exact solutions, the semidiscrete against the fully-discrete solutions, and the fully-discrete solutions
Ferdowsi University of Mashhad, 2024
This article presents a parameter uniform convergence numerical scheme for solving time fractiona... more This article presents a parameter uniform convergence numerical scheme for solving time fractional order singularly perturbed parabolic convectiondiffusion differential equations with a delay. We give a priori bounds on the exact solution and its derivatives obtained through the problem's asymptotic analysis. The Euler's method on a uniform mesh in the time direction
Ferdowsi University of Mashhad, 2024
An improvised collocation scheme is applied for the numerical treatment of the nonlinear generali... more An improvised collocation scheme is applied for the numerical treatment of the nonlinear generalized Burgers-Fisher's (gBF) equation using splines of degree three. In the proposed methodology, some subsequent rectifications are done in the spline interpolant, which resulted in the magnification of the order of convergence along the space direction. A finite difference approach is followed to integrate the time direction. Von Neumann methodology is opted to discuss the stability of the method. The error bounds and convergence study show that the technique has (s 4 + ∆t 2) order of convergence. The correspondence between the approximate and analytical solutions is shown by graphs, plotted using MATLAB and by evaluating absolute error.
Ferdowsi University of Mashhad, 2024
In this work, we propose a mathematical model that describes citizens' behavior toward a product,... more In this work, we propose a mathematical model that describes citizens' behavior toward a product, where individuals are generally divided into three main categories: potential consumers, boycotters who abstain from it for
Ferdowsi University of Mashhad, 2024
In this work, we propose a mathematical model that describes citizens' behavior toward a product,... more In this work, we propose a mathematical model that describes citizens' behavior toward a product, where individuals are generally divided into three main categories: potential consumers, boycotters who abstain from it for
Ferdowsi University of Mashhad, 2024
An improved imperialist competitive algorithm for solving an inverse form of the Huxley equation.... more An improved imperialist competitive algorithm for solving an inverse form of the Huxley equation. Iran.
Ferdowsi University of Mashhad, 2024
We study the calculus of variations problem in the presence of a system of differential-integral ... more We study the calculus of variations problem in the presence of a system of differential-integral (D-I) equations. In order to identify the necessary optimality conditions for this problem, we derive the so-called D-I Euler-Lagrange equations. We also generalize this problem to other cases, such as the case of higher orders, the problem of optimal control, and we derive the so-called D-I Pontryagin equations. In special cases, these formulations lead to classical Euler-Lagrange equations. To illustrate our results, we provide simple examples and applications such as obtaining the minimum power for an RLC circuit.
Ferdowsi University of Mashhad, 2024
In this paper, a singularly perturbed one-dimensional initial boundary value problem of a quasili... more In this paper, a singularly perturbed one-dimensional initial boundary value problem of a quasilinear Sobolev-type equation is presented. The nonlinear term of the problem is linearized by Newton's linearization method. Time derivatives are discretized by implicit Euler's method on nonuniform step size. A uniform trigonometric B-spline collocation method is used to treat the spatial variable. The convergence analysis of the scheme is proved, and the accuracy of the method is of order two in space and order one in time direction, respectively. To test the efficiency of the method, a model example is demonstrated. Results of the scheme are presented in
Ferdowsi University of Mashhad, 2024
In this article, we explore the discontinuous Galerkin finite element method for two-parametric s... more In this article, we explore the discontinuous Galerkin finite element method for two-parametric singularly perturbed convection-diffusion problems with a discontinuous source term. Due to the discontinuity in the source term, the problem typically shows a weak interior layer. Also, the presence of multiple perturbation parameters in the problem causes boundary layers on both sides of the boundary. In this work, we develop the nonsymmetric discontinuous Galerkin finite element method with interior penalties to handle the layer phenomenon. With the use of a typical Shishkin mesh, the domain is discretized, and a uniform error estimate is obtained. Numerical experiments are conducted to validate the theoretical conclusions.
Ferdowsi University of Mashhad, 2024
In the present paper, we precisely conduct a quantum calculus method for the numerical solutions ... more In the present paper, we precisely conduct a quantum calculus method for the numerical solutions of PDEs. A nonlinear Schrödinger equation is considered. Instead of the known classical discretization methods based on the finite difference scheme, Adomian method, and third modified ver-sions, we consider a discretization scheme leading to subdomains according to q-calculus and provide an approximate solution due to a specific value of the parameter q. Error estimates show that q-calculus may produce effi-cient numerical solutions for PDEs. The q-discretization leads effectively to higher orders of convergence provided with faster algorithms. The numer-ical tests are applied to both propagation and interaction of soliton-type solutions.
Ferdowsi University of Mashhad, 2023
We suggest an a priori method by introducing the concept of A Pequitable efficiency. The preferen... more We suggest an a priori method by introducing the concept of A Pequitable efficiency. The preferences matrix A P , which is based on the partition P of the index set of the objective functions, is given by the decision-maker. We state the certain conditions on the matrix A P that guarantee the preference relation ⪯ eA P to satisfy the strict monotonicity and strict P-transfer principle axioms. A problem most frequently encountered in multiobjective optimization is that the set of Pareto optimal solutions provided by the optimization process is a large set. Hence, the decision-making based on selecting a unique preferred solution becomes difficult. Considering models with A r P-equitable efficiency and A ∞ P-equitable efficiency can help the decision-maker for overcoming this difficulty, by shrinking the solution set.
Ferdowsi University of Mashhad, 2023
A mathematical collocation solution for generalized Burgers-Huxley and generalized Burgers-Fisher... more A mathematical collocation solution for generalized Burgers-Huxley and generalized Burgers-Fisher equations has been monitored using the weighted residual method with Hermite splines. In the space direction, quintic Hermite splines are introduced, while the time direction is discretized using a finite difference approach. The technique is determined to be unconditionally stable, with order (h 4 + △t) convergence. The technique's efficacy is tested using nonlinear partial differential equations. Two problems of the generalized Burgers-Huxley and Burgers-Fisher equations have been solved using a finite difference scheme as well as the quintic Hermite collocation method (FDQHCM) with varying impacts. The FDQHCM computer codes are written in MATLAB without transforming the nonlinear term to a linear term. The numerical findings are reported in weighted norms and in discrete form. To assess the technique's applicability, numerical and exact values are compared, and a reasonably good agreement is recognized between the two.
Ferdowsi University of Mashhad, 2023
Like the Polak-Ribière-Polyak (PRP) and Hestenes-Stiefel (HS) methods, the classical Liu-Storey (... more Like the Polak-Ribière-Polyak (PRP) and Hestenes-Stiefel (HS) methods, the classical Liu-Storey (LS) conjugate gradient scheme is widely believed to perform well numerically. This is attributed to the in-built capability of the method to conduct a restart when a bad direction is encountered. However, the scheme's inability to generate descent search directions, which is vital for global convergence, represents its major shortfall. In this article, we present an LS-type scheme for solving system of monotone nonlinear equations with convex constraints. The scheme is based on the approach by Wang et al. (2020) and the projection scheme by Solodov and Svaiter (1998). The new scheme satisfies the important condition for global convergence and is suitable for non-smooth nonlinear problems. Furthermore, we demonstrate the method's application in restoring blurry images in compressed sensing. The scheme's global convergence is established under mild assumptions and preliminary numerical results show that the proposed method is promising and performs better than two recent methods in the literature.
Ferdowsi University of Mashhad, 2023
To solve challenges occurred in the existence of large sets of data, recent improvements of machi... more To solve challenges occurred in the existence of large sets of data, recent improvements of machine learning furnish promising results. Here to propose a tool for predicting lesser liquid credit default swap (CDS) rates in the presence of CDS spreads over a large period of time, we investigate different machine learning techniques and employ several measures such as the root mean square relative error to derive the best technique, which is useful for this type of prediction in finance. It is shown that the nearest neighbor is not only efficient in terms of accuracy but also desirable with respect to the elapsed time for running and deploying on unseen data.
Ferdowsi University of Mashhad, 2023
This paper focuses on the result of inclined angle on bioconvection of porous media bounded by ca... more This paper focuses on the result of inclined angle on bioconvection of porous media bounded by cavity wall square enclosure filled with both nanofluid and gyrotactic microorganisms passing through the media with pores. The dimensionless velocity, temperature, concentration, and mass transformation equations are solved by using the weighted residual Galerkin's finite element method. The result of the inclination angle from δ = 0 • to δ = 180 • in a square cavity is interpreted. The outcomes of inclination on various key parameters, such as Rayleigh number, bioconvective Rayleigh number, Peclet number, Brownian motion, and the ratio of buoyancy, are discussed. Furthermore, the mean Nusselt number, Sherwood number, and density number are discussed at vertical walls.
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Papers by Iranian journal of Numerical Analysis and Optimization