Numerical solutions of heat equations with homotopy perturbation method

In this study, numerical solutions of linear and non-linear partial differential equations of parabolic type are investigated. To this purpose, we first solved the linear heat equation numerically and analytically with Crank-Nicolson, Homotopy Perturbation and Adomian Decomposition methods, and then compared the numerical results. As a result of this comparison, it was seen that Homotopy Perturbation and Adomian Decomposition methods are more stable than the Crank-Nicolson method. Also, the second order nonlinear partial differential equations of parabolic type that we discussed were solved numerically by Newton's linearization and Homotopy Perturbation methods. When the results were compared, it was seen that the results were stable and convergent.