Operator Splitting Solution of Equal Width Wave Equation Based on the Lie-Trotter and Strang Splitting Methods

Abstract

In the present work, we have applied four different algoritms based on the Lie-Trotter and Strang splitting methods to obtain numerical solution of Equal Width (EW) equation. For this purpose, EW equation is split up into two sub equation which one is linear and the other is nonlinear and then cubic B-spline collocation finite element method applied to each sub equation. The main advantage of this method is to obtain simpler and easier to solve sub-equations. The accuracy of the suggested method is displayed by calculating error norms $L_{2}$, $L_{\infty }$ and conservation laws on the solution of a single wave motion. It was seen that cubic B-spline collocation schemes obtained via Lie-Trotter and Strang splitting methods led to\ lower error norms and quate easy to implement. The stability analysis of obtained schemes are investigated by von Neumann (Fourier Series) method in accordance with the structure of splitting methods. We considered single wave motion and Maxwellian initial pulse to examine the numerical solutions of the EW equation and to compare it with other studies.

Keywords

• Operator splitting method,Lie-Trotter splitting,Strang splitting,Equal width equation,Collocation method

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