Numerical Solutions of the Gardner Equation via Trigonometric Quintic B-spline Collocation Method

Özet

The main purpose of this paper is to get the numerical solutions of the Gardner equation which are widely used in various disciplines. For this purpose, the time integration of the system is achieved by the classical Crank-Nicolson method owing to its large stability region. Space discretization is done by using the trigonometric quintic B-spline functions. Thus the Gardner equation turns into a penta diagonal matrix equation and the Thomas algorithm is applied owing to lower cost of computation when compared Gauss or Gauss-Jordan elimination methods.