He's homotopy perturbation method for solving the shock wave equation

Abstract

In this article, we discuss the analytic solution of the fully developed shock waves. The homotopy perturbation method is used to solve the shock wave equation, which describes the flow of gases. Unlike the various numerical techniques, which are usually valid for short period of time, the solution of the presented equation is analytic for 0 < t < ∞. The results presented converge very rapidly, indicating that the method is reliable and accurate.

Keywords:

• the homotopy perturbation method
• shock wave equations
• soliton solutions
• conservation law

AMS Subject Classifications:

• 76M45
• 76L05
• 37K40
• 35L65

Acknowledgements

The authors thank the unknown referees for their constructive comments and suggestions.