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RISLegendre Approximation for Solving Linear HPDEs and Comparison with Taylor and Bernoulli Matrix Methods
ABSTRACT
The aim of this study is to give a Legendre polynomial approximation for the solution of the second order linear hyper-bolic partial differential equations (HPDEs) with two variables and constant coefficients. ...
Numerical solution of time-dependent diffusion equations with nonlocal boundary conditions via a fast matrix approach
This article contributes a matrix approach by using Taylor approximation to obtain the
numerical solution of one-dimensional time-dependent parabolic partial differential equations
(PDEs) subject to nonlocal ...
Convergence analysis of Bernoulli matrix aproach for one-dimensional matrix hyperbolic equations of the first order
In this paper, an approximate approach based on Bernoulli operational matrices has been
presented to obtain the numerical solution of first-order matrix hyperbolic partial differential
equations under the ...
A new Bernoulli matrix method for solving second order linear partial differential equations with the convergence analysis
In this paper, a new matrix approach for solving second order linear partial differential equations (PDEs) under given initial conditions has been proposed. The basic idea includes integrating from the considered PDEs and ...
An optimized derivative-free form of the Potra–Pták method
Abstract
In this paper, we discuss iterative methods for solving univariate nonlinear equations. First of all, we construct a family of methods with optimal convergence rate 4 based upon the Potra–Pták scheme ...
Numerical Solution of Linear HPDEs Via Bernoulli Operational Matrix of Differentiation and Comparison with Taylor Matrix Method
Abstract
In this paper a new matrix approach for solving linear hyperbolic partial differential equations (HPDEs) is presented. The method is based on the Bernoulli expansion of two-variable functions, which consists ...
Numerical solution of weakly singular Fredholm integral equations via generalization of the Euler–Maclaurin summation formula
Since the classical Euler–Maclaurin summation formula may not be applied for approximating singular integrals, we can not use this formula for obtaining the numerical solution of weakly singular Fredholm integral equations. ...
Numerical Solution of Two-Dimensional Volterra Integral Equations by Spectral Galerkin Method
In this paper, we present ultra spherical spectral discontinuous Galerkin method for solving the two-dimensional volterra integral equation (VIE) of the second kind. The Gauss-Legendre quadrature rule is used to ap- proximate ...
A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain
This paper contributes a new matrix method for the solution of high-order linear complex differential equations with variable coefficients in rectangular domains under the considered initial conditions.On the basis of the ...
Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications
This paper introduces Fourier operational matrices of differentiation and transmission for solving high-order linear differential and difference equations with constant coefficients. Moreover, we extend our methods for ...