Solution of Wave Equations and Heat Equations Using HPM
In this paper, the homotopy perturbation method (HPM) has been used to solve some wave equations and a few heat equations. The resultant solution helps to substantiate that HPM is a useful and robust mechanism to solve these equations. An accurate approximation is possible while solving complex and complicated problems using semi-analytical methods, an example of which is the HPM. However, we consider the boundary conditions as one-dimensional when we use this method, and hence these approximations can be considered only for a small range. HPM was developed by J. H. He for solving wave and heat equations. To obtain accurate results for these equations using HPM, standard homotopy technique is merged with the perturbation technique along with some modifications.
- 10.J.H. He, Non-perturbative methods for strongly nonlinear problems, Dissertation, de-Verlag in Internet GmbH, Berlin (2006).Google Scholar