Two Effective Numerical Approaches for Equal Width Wave (EW) Equation Using Lie-Trotter Splitting Technique

Abstract

In this work, approximate solutions of the EW equation are obtained by two influential numerical schemes. For the first and second method, after splitting equal width wave (EW) equation in time, it is solved by Lie- Trotter splitting technique via quintic B-spline Collocation and cubic B-spline Lumped Galerkin FEMs and the suited finite difference approaches for space and time discretizations respectively. Stability analysis of schemes is shown and both schemes are implemented to two example. The acquired numerical results are compared with those in the literature with the help of the error norms and conservation features. It is seen that the error norms are quite small, the present conservation constants are consistent according to the results compared.

Keywords

• B-splines
• Collocation method
• Lumped Galerkin method
• Equal Width Equation
• Lie- Trotter splitting

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