The analytical and a higher-accuracy numerical solution of a free boundary problem in a class of discontinuous functions
type: Item
instance of: scholarly article
title: The analytical and a higher-accuracy numerical solution of a free boundary problem in a class of discontinuous functions
zbMATH Open document ID: 1264.35286
DOI: 10.1155/2012/791026
author: Bahaddin Sinsoysal
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: A new method is suggested for obtaining the exact and numerical solutions of the initial-boundary value problem for a nonlinear parabolic type equation in the domain with the free boundary. With this aim, a special auxiliary problem having some advantages over the main problem and being equivalent to the main problem in a definite sense is introduced. The auxiliary problem allows us to obtain the weak solution in a class of discontinuous functions. Moreover, on the basis of the auxiliary problem a higher-resolution numerical method is developed so that the solution accurately describes all physical properties of the problem. In order to extract the significance of the numerical solutions obtained by using the suggested auxiliary problem, some computer experiments are carried out.
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35C08
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 65M70
zbMATH DE Number: 6173580
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/791026
OpenAlex ID: W2059934474
Wikidata QID: Q58911934
cites work: Q3961220
cites work: The problem of the three-dimensional localization of thermal perturbations in the theory of non-linear heat conduction
cites work: Q3284846
cites work: Q5339539
cites work: On the numerical solution of some sets of differential equations for problems of Stefan's type
cites work: The numerical solution of a one-dimensional problem for equations of non-stationary filtration
cites work: A difference method with front straightening for solving Stefan-type problems
cites work: Q3324968
cites work: Q3073820
description: scientific article; zbMATH DE number 6173580