Structure of analytical and numerical wave solutions for the Ito integro-differential equation arising in shallow water waves

Abstract

In this research, by implementing modified analytical and numerical methods, the construction of the analytical and numerical wave solutions for the Ito integro-differential dynamical equation are obtained. The central finite differences are employed to derive the numerical solutions of this equation. We applied the Taylor expansion to test the accuracy of the numerical solutions. We invoke the Von Neumann’s stability to explore the stability. The comparison between the exact and numerical results is successfully obtained. We provide some graphical representations to illustrate this comparison and to show the behaviour of the travelling wave solutions. The error which arises from the performance of the used numerical method is investigated. The used methods can be utilized to deal with more nonlinear partial differential equations.

Keywords

• Ito equation
• The improved F-expansion approach
• Riccati equation
• Central finite differences
• Travelling wave solution
• Numerical solution