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## Publications

Publications (16)

In this paper we introduce a block-by-block method for the numerical solution of multi-term fractional differential equations (MFDEs). The main idea is to convert a MFDE to a Volterra integral equation of weakly singular type, to which a well known block-by-block method is applied. We also provide the error analysis and convergence of the method. F...

The study introduces a fractional mathematical model in the Caputo sense for hematopoietic stem cell-based therapy, utilizing generalized Bernoulli polynomials (GBPs) and operational matrices to solve a system of nonlinear equations. The significance of the study lies in the potential therapeutic applications of hematopoietic stem cells (HSCs), par...

In this paper, a mathematical model of the eye corneal shape is introduced which is a nonlinear boundary value problem. This boundary value problem is converted to a nonlinear integral equation and by means of the collocation method, the problem is reduced into a system of the nonlinear algebraic equations. The approximate solutions are obtained by...

The main purpose of this paper is to propose a block by block method for a class of the Volterra integral equations (VIEs) with double constant delays. The convergence analysis is established and the fifth order of convergence is obtained. Then the stability analysis of the presented method is carried out with respect to the basic test equation y(t...

In this paper we propose a numerical method for nonlinear second kind Volterra integral equations (VIEs) with (vanishing) proportional delays qt (0<q<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidema...

Various numerical methods have been proposed for the solution of weakly singular Volterra integral equations but, for the most part, authors have dealt with linear or one-dimensional weakly singular Volterra integral equations, or have assumed that these equations have smooth solutions. The main purpose of this paper is to propose and analyse a num...

Mixed Volterra-Fredholm integral equations can arise from mathematical modelling of the spatio-temporal development of an epidemic. In this paper a hybrid Legendre block-pulse method is used to provide solutions to a general integral equation of this type. The main idea of this approach is to reduce a Volterra-Fredholm integral equation to a system...

This paper is concerned with the numerical solution of the mixed Volterra-Fredholm integral equations by using a version of the block by block method. This method efficient for linear and nonlinear equations and it avoids the need for spacial starting values. The convergence is proved and finally performance of the method is illustrated by means of...

In this paper, a numerical method for solving the linear and nonlinear Fredholm integral equations is proposed. In this method the solution of these equations are approximated by Romberg quadrature rule. Also, the convergence of the method is proved and some numerical examples are solved to investigate the applicability and simplicity of the method...

In this study we propose a numerical method for linear and nonlinear neutral pantograph equations. Most of the proposed numerical methods for this kind of equations was mainly introduced only for linear equations, but in the present paper we generalize our method for nonlinear cases, too. We prove that the numerical solution is convergent and some...

In this paper, a collocation method by using Clenshaw–Curtis points is proposed to solve the Fredholm integral equations (FIEs) with highly oscillatory kernels. The collocation method is being applied to graded and uniform meshes. Due to the highly oscillatory kernels of integral equations, the discretized collocation equation will lead to the comp...

The aim of the present paper is to introduce a block by block method for solving system of nonlinear Volterra integral equations with continuous kernels and system of Abel integral equations. We prove convergence of the method and show that its convergence order is at least six. To illustrate performance of the method, numerical experiments are pre...

In this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear Volterra integral equations of the first and second kinds, which avoids from using starting values. An existence and uniqueness theorem is proved and convergence is verified by using an appropriate variety of the Gronwall inequality. Applicatio...

We investigate the numerical solutions of nonlinear Volterra integral equations by the block-by-block method especially useful for the solution of integral equations on large-size intervals. A convergence theorem is proved showing that the method has at least sixth order of convergence. Finally, the performance of the method is illustrated by some...

In this paper, we propose an efficient numerical method for solving systems of linear and nonlinear integral equations of the first and second kinds, which avoids the need for special starting values. The method has also the advantages of simplicity of application and at least six order of convergence. A convergence analysis is given and accuracy o...

The approach given in this paper leads to numerical methods for solving system of Volterra integral equations which avoid the need for special starting procedures. The method has also the advantages of simplicity of application and at least four order of convergence which is easy to achieve. Also, at each step we get four unknowns simultaneously. A...