Open Access
Subscription or Fee Access
A New MATLAB Implementation and Analysis of A Moving Grid Method For Systems of One-Dimensional Time-Dependent Partial Differential Equations Based on The Equidistribution Principle
Sangare Boureima, Diallo Ouateni, Some Longin
Abstract
In the past several years, several numerical techniques have been developed to solvetime-dependent partial diffrential equations (PDEs) in one dimension having solutions with steep gradients in space and in time. One of these techniques, a moving grid method, has been coupled with a spatial discretization method that automatically discretizes the spatial part of the user-defined PDE following the method of line approach. The objective of this paper is to report on the development of a Method of Lines (MOL) toolbox within MATLAB, and especially, on the implementation and test of a moving grid graphical user interface based on the equidistribution principle. This new user-interface includes various spatial approximation schemes based on finite differences and slope limiters, the choice between several monitor functions, automatic grid adaptation to the initial condition and provides a relatively easy tuning for the non-expert user. Several issues, including the sensitivity of the numerical results to the tuning parameters, are discussed. Some numerical examples characterized by solutions with steep moving fronts, are investigated so as to demonstrate the algorithm performance and to illustrate the simple and effective use of this software interface.
Keywords
partial differential equations (PDEs), moving grids, finite difference methods (FDMs), method of lines (MOL), monitor functions.
Full Text:
PDF
Disclaimer/Regarding indexing issue:
We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.