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

TOK ONARCAN A., ADAR N., DAĞ İ.

COMPUTATIONAL & APPLIED MATHEMATICS, cilt.37, sa.5, ss.6848-6869, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 5
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s40314-018-0713-4
  • Dergi Adı: COMPUTATIONAL & APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.6848-6869
  • Anahtar Kelimeler: Finite-element method, Collocation, B-spline, Reaction-diffusion
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

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.