NUMERICAL SOLUTIONS OF REACTION-DIFFUSION EQUATION SYSTEMS WITH TRIGONOMETRIC QUINTIC B-SPLINE COLLOCATION ALGORITHM

In this study, trigonometric quintic B-spline collocation method is constructed for computing numerical solutions of the reaction-diffusion system (RDS). Schnakenberg, Gray-Scott and Brusselator models are special cases systems considered as examples in paper. Crank-Nicolson formulae used time discretization generalized RDS nonlinear terms time-discretized form linearized using Taylor expansion. The fully integration carried out based on B-splines. tested different problems to illustrate accuracy. error norms calculated linear problem whereas relative given problems. Both simple easy algorithms illustrated give also graphical representation efficient presented RDSs. Combination B-splines shown present successfully. With method, it possible get approximate well their derivatives up an order four domain.