An efficient spectral approximation for solving several types of parabolic PDEs with nonlocal boundary conditions
type: Item
instance of: scholarly article
title: An efficient spectral approximation for solving several types of parabolic PDEs with nonlocal boundary conditions
zbMATH Open document ID: 1407.65228
DOI: 10.1155/2014/369029
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: The problem of solving several types of one-dimensional parabolic partial differential equations (PDEs) subject to the given initial and nonlocal boundary conditions is considered. The main idea is based on direct collocation and transforming the considered PDEs into their associated algebraic equations. After approximating the solution in the Legendre matrix form, we use Legendre operational matrix of differentiation for representing the mentioned algebraic equations clearly. Three numerical illustrations are provided to show the accuracy of the presented scheme. High accurate results with respect to the Bernstein Tau technique and Sinc collocation method confirm this accuracy.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 7016274
Wikidata QID: Q59064693
author: Emran Tohidi
author: Adem Kilicman
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/369029
OpenAlex ID: W2043316676
cites work: Galerkin method applied to a parabolic evolution problem with nonlocal boundary conditions
cites work: A numerical solution for non-classical parabolic problem based on Chebyshev spectral collocation method
cites work: A tau method approach for the diffusion equation with nonlocal boundary conditions
cites work: The operational matrices of Bernstein polynomials for solving the parabolic equation subject to specification of the mass
cites work: Solving a parabolic PDE with nonlocal boundary conditions using the sinc method
cites work: Numerical solution of a nonclassical parabolic problem: an integro-differential approach
cites work: A Legendre-Gauss collocation method for neutral functional-differential equations with proportional delays
cites work: A collocation method based on the Bernoulli operational matrix for solving nonlinear BVPs which arise from the problems in calculus of variation
cites work: A collocation method based on the Bernoulli operational matrix for solving high-order linear complex differential equations in a rectangular domain
description: scientific article; zbMATH DE number 7016274