Trigonometric cubic B-spline collocation algorithm for numerical solutions of reaction-diffusion equation systems

TOK ONARCAN A., ADAR N., DAĞ İ.

COMPUTATIONAL & APPLIED MATHEMATICS, vol.37, no.5, pp.6848-6869, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 5
  • Publication Date: 2018
  • Doi Number: 10.1007/s40314-018-0713-4
  • Journal Name: COMPUTATIONAL & APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.6848-6869
  • Keywords: Finite-element method, Collocation, B-spline, Reaction-diffusion
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

An algorithm for the reaction-diffusion system including model problems Brusselator, Schnakenberg and Gray-Scott is introduced. The integration of the system is managed by combining the Crank-Nicolson method in time and the cubic trigonometric B-spline collocation method in space. Our aim here is to provide a new code to understand and implement reaction-diffusion-type events. Some problems chosen from the literature to illustrate the efficiency of the algorithm are studied for each model problem.