A new non-polynomial spline method for solution of linear and non-linear third order dispersive equations

Abstract

Abstract In this paper, a new three-level implicit method is developed to solve linear and non-linear third order dispersive partial differential equations. The presented method is obtained by using exponential quartic spline to approximate the spatial derivative of third order and finite difference discretization to approximate the first order spatial and temporal derivative. The developed method is tested on four examples and the results are compared with other methods from the literature, which shows the applicability and feasibility of the presented method. Furthermore, the truncation error and stability analysis of the presented method are investigated, and graphical comparison between analytical and approximate solution is also shown for each example.

Keywords

• Spline function approximation
• Third order dispersive equation
• Stability analysis
• Korteweg-de Vries (KdV) equation
• Soliton