AN EFFICIENT NUMERICAL METHOD BASED ON CUBIC B-SPLINE FOR TIME DEPENDENT PROBLEM WITH SMALL PARAMETER

Kelthoum Lina Redouane, Nouria Arar, Qasem Al-Mdallal

Research output: Contribution to journalArticlepeer-review

Abstract

This work is devoted to the development of a Galerkin-type approximation of the solution of parabolic reaction-diffusion problems, utilizing cubic B-Spline functions and a finite difference scheme. An error estimate for the semi discrete weak Galerkin scheme is established. A Von Neumann stability study of the proposed fully discrete Crank Nicolson scheme is also performed. In addition, examples are used to validate the proposed approximation. The numerical results produced demonstrate the procedure’s efficacy and are in good agreement with the exact solution.

Original languageEnglish
Pages (from-to)131-152
Number of pages22
JournalProceedings of the Institute of Mathematics and Mechanics
Volume48
Issue numberSpecial Issue
DOIs
Publication statusPublished - 2022

Keywords

  • Cubic B-splines
  • Finite Difference Scheme
  • Finite differences
  • Galerkin method
  • Parabolic problem

ASJC Scopus subject areas

  • Mathematics(all)

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