Farshid Mirzaee
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View article: On two‐dimensional weakly singular fractional partial integro‐differential equations and dual Bernstein polynomials
On two‐dimensional weakly singular fractional partial integro‐differential equations and dual Bernstein polynomials Open
This article presents an efficient numerical scheme based on some properties of dual Bernstein operational matrices for a class of linear and nonlinear two‐dimensional weakly singular fractional partial integro‐differential equations (WSFP…
View article: An efficient cubic B‐spline and bicubic B‐spline collocation method for numerical solutions of multidimensional nonlinear stochastic quadratic integral equations
An efficient cubic B‐spline and bicubic B‐spline collocation method for numerical solutions of multidimensional nonlinear stochastic quadratic integral equations Open
This paper aims to develop a novel numerical approach on the basis of B‐spline collocation method to approximate the solution of one‐dimensional and two‐dimensional nonlinear stochastic quadratic integral equations. The proposed approach i…
View article: Issue Information
Issue Information Open
An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spect…
View article: Issue Information
Issue Information Open
An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spect…
View article: Numerical Solution of Weakly Singular Ito-Volterra Integral Equations via Operational Matrix Method based on Euler Polynomials
Numerical Solution of Weakly Singular Ito-Volterra Integral Equations via Operational Matrix Method based on Euler Polynomials Open
Numerical Solution of Weakly Singular Ito-Volterra Integral Equations via Operational Matrix Method based on Euler Polynomials
View article: Convergence of Legendre wavelet collocation method for solving nonlinear Stratonovich Volterra integral equations
Convergence of Legendre wavelet collocation method for solving nonlinear Stratonovich Volterra integral equations Open
In this paper, we apply Legendre wavelet collocation method to obtain the approximate solution of nonlinear Stratonovich Volterra integral equations. The main advantage of this method is that Legendre wavelet has orthogonality property and…
View article: Convergence of 2D-orthonormal Bernstein collocation method for solving 2D-mixed Volterra–Fredholm integral equations
Convergence of 2D-orthonormal Bernstein collocation method for solving 2D-mixed Volterra–Fredholm integral equations Open
In this paper, an efficient numerical method is used for solving 2D-mixed Volterra–Fredholm integral equations. This method is based on 2D-orthonormal Bernstein polynomials (2D-OBPs) together with collocation method. This approach is appli…
View article: Numerical solution of nonlinear Fredholm-Volterra integral equations via Bell polynomials
Numerical solution of nonlinear Fredholm-Volterra integral equations via Bell polynomials Open
In this paper, we propose and analyze an efficient matrix method based on Bell polynomials for numerically solving nonlinear Fredholm- Volterra integral equations. For this aim, first we calculate operational matrix of integration and prod…
View article: Using operational matrix for numerical solution of fractional differential equations
Using operational matrix for numerical solution of fractional differential equations Open
In this article, we have discussed a new application of modification of hat functions on nonlinear multi-order fractional differential equations. The operational matrix of fractional integration is derived and used to transform the main eq…
View article: Application of modified hat functions for solving nonlinear quadratic integral equations
Application of modified hat functions for solving nonlinear quadratic integral equations Open
A numerical method to solve nonlinear quadratic integral equations (QIE) is presented in this work. The method is based upon modification of hat functions (MHFs) and their operational matrices. By using this approach and the collocation po…
View article: Numerical method for solving optimal control problem of the linear differential systems with inequality constraints
Numerical method for solving optimal control problem of the linear differential systems with inequality constraints Open
In this paper, an efficient method for solving optimal control problems of the linear differential systems with inequality constraint is proposed. By using new adjustment of hat basis functions and their operational matrices of integration…