A numerical aproach to dispersion-dissipation-reaction model: third order KdV-Burger-Fisher equation

Abstract

In this study, an efficient numerical method is applied to KdV-Burger-Fisher equation
which is one of the dispersion-dissipation–reaction model. The present method is based
on the collocation method whose weight functions are taken from the family of the Dirac
delta functions in finite element methods. The element functions are selected as quintic
trigonometric B-spline basis. The error norms L2 and L∞ are calculated to measure
the efficiency of the method. Numerical solutions and error norms which are obtained
via collocation method and trigonometric basis are presented in tables and simulations
of the solutions are exhibited as well. Additionally, stability analysis is investigated.