New modification of the HPM for numerical solutions of the sine-Gordon and coupled sine-Gordon equations

Abstract

We present an efficient modification of the He's homotopy perturbation method that will facilitate the calculations. We apply this modification to solve sine-Gordon and coupled sine-Gordon equations, numerically. The new modification introduces a promising tool for many non-linear problems. The present method performs extremely well in terms of accuracy, efficiency, simplicity and reliability.

Keywords:

• homotopy perturbation method
• modified homotopy perturbation method
• sine-Gordon equation
• coupled sine-Gordon equation
• Adomian polynomial

2000 AMS Subject Classification :

• 65N99
• 65M99
• 65Z05