A non-separable solution of the diffusion equation based on the Galerkin's method using cubic splines
type: Item
instance of: scholarly article
title: A non-separable solution of the diffusion equation based on the Galerkin's method using cubic splines
zbMATH Open document ID: 1204.65125
author: Sumit K. Garg
published in: Applied Mathematics and Computation
publication date: 2010-11-18T00:00:00Z
review text: The authors present an algorithm to solve the two dimensional diffusion equation based on the Galerkin method where a collocation method is applied to the initial condition using bi-cubic \(B\)-splines [cf. \textit{I. Dağ, B. Saka} and \textit{A. Boz}, Appl. Math. Comput. 166, No.~3, 506--522 (2005; Zbl 1073.65099)]. The proposed method is applicable whenever the initial condition is given in an unbounded region or with a free boundary condition. It is shown that for the diffusion equation in an unbounded region, there is a very simple effective solution for the time dependent equation.
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 5817267
zbMATH Keywords: diffusion equation
zbMATH Keywords: Galerkin method
zbMATH Keywords: bi-cubic splines
zbMATH Keywords: collocation method
zbMATH Keywords: non-separable solution
zbMATH Keywords: algorithm
zbMATH Keywords: free boundary condition
zbMATH Keywords: unbounded region
MaRDI profile type: Publication
full work available at URL: j.amc.2010.05.018
OpenAlex ID: W1981697759
cites work: Heatlet approach to diffusion equation on unbounded domains
cites work: 2D parallel and stable group explicit finite difference method for solution of diffusion equation
cites work: On the numerical solution of the diffusion equation with variable space operator
cites work: B-spline Galerkin methods for numerical solutions of the Burgers' equation
cites work: Q3425498
DOI: 10.1016/J.AMC.2010.05.018
description: scientific article; zbMATH DE number 5817267