Wannika Sawangtong and Panumart Sawangtong

This research paper deals with the new method used to find the approximate analytical solutions of the initial-boundary value problems (IBVPs). This method is named the Sawangtong’s Green function homotopy perturbation method (SGHPM) combining the Green’s function method with the homotopy perturbation method. The SGHPM process simple, easy, and effective. Therefore, the SGHPM is a technique which is powerful and efficient for finding the solutions of IBVPs as SGHPM applications such as the heat equation problem with the Dirichlet boundary condition, the heat equation problem with the Neumann boundary condition, the heat equation problem with the periodic boundary condition, and the parabolic partial differential equation with variable coefficients.