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

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.

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