Journal ArticleDOI
Numerical solution of Volterra–Fredholm integral equations using the collocation method based on a special form of the Müntz–Legendre polynomials
Neda Negarchi,Kazem Nouri +1 more
Reads0
Chats0
TLDR
A computational technique based on a special family of the Muntz–Legendre polynomials to solve a class of Volterra–Fredholm integral equations via the Chebyshev–Gauss–Lobatto points, so that the system matrix coefficients are obtained by the least squares approximation method.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2018-12-15. It has received 17 citations till now. The article focuses on the topics: Jacobi polynomials & Collocation method.read more
Citations
More filters
Journal ArticleDOI
Application Local Polynomial and Non-polynomial Splines of the Third Order of Approximation for the Construction of the Numerical Solution of the Volterra Integral Equation of the Second Kind
TL;DR: In this paper, the application of polynomial and non-polynomial splines to the solution of nonlinear Volterra integral equations is discussed. And the results of the numerical experiments are presented.
Journal ArticleDOI
Müntz–Legendre neural network construction for solving delay optimal control problems of fractional order with equality and inequality constraints
TL;DR: An artificial intelligence approach using neural networks is described to solve a class of delay optimal control problems of fractional order with equality and inequality constraints using a functional link neural network based on the Müntz–Legendre polynomial.
Journal ArticleDOI
Solving a System of Fractional-Order Volterra-Fredholm Integro-Differential Equations with Weakly Singular Kernels via the Second Chebyshev Wavelets Method
TL;DR: This paper solves a system of fractional-order Volterra–Fredholm integro-differential equations with weakly singular kernels by means of the second Chebyshev wavelet and its operational matrix and obtains approximate solutions from the algebraic system corresponding to the main system.
Journal ArticleDOI
Applying the three‐dimensional block‐pulse functions to solve system of Volterra–Hammerstein integral equations
Journal ArticleDOI
A hybrid approach established upon the Müntz‐Legender functions and 2D Müntz‐Legender wavelets for fractional Sobolev equation
TL;DR: In this paper , a hybrid technique for finding approximation solutions of the fractional 2D Sobolev equation is proposed, where the Müntz-Legender functions and the wavelet functions are used to approximate the solution of the problem under consideration in the time and spatial directions.
References
More filters
Book
Computational Methods for Integral Equations
L. M. Delves,J. L. Mohamed +1 more
TL;DR: In this article, the authors introduce the theory of linear integral equations of the second kind and the Nystrom (quadrature) method for Fredholm equations of second kind, and present an analysis of the Galerkin method with orthogonal basis.
Book
Polynomials and Polynomial Inequalities
Peter Borwein,Tamás Erdélyi +1 more
TL;DR: Inequalities in Muntz Spaces and Rational Function Spaces have been investigated in this article, where the authors show that inequalities for Polynomials with Constraints imply Orthogonality and Irrationality.
Journal ArticleDOI
Legendre wavelets method for the nonlinear Volterra-Fredholm integral equations
TL;DR: A numerical method for solving the nonlinear Volterra-Fredholm integral equations is presented, based upon Legendre wavelet approximations and the Gaussian integration method.
Journal ArticleDOI
Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials
TL;DR: This paper presents a computational technique based on the collocation method and Muntz polynomials for the solution of fractional differential equations with superior accuracy and exponential convergence.