Laplace Homotopy Perturbation Method for Solving Fourth Order Parabolic Partial Differential Equations with Variable Coefficients

In this paper, we present a reliable combination of the Laplace transform and Homotopy perturbation method to solve one-dimensional fourth-order parabolic linear partial differential equations with variable coefficients. Some cases of one-dimensional fourth-order parabolic linear partial differential equations are considered to illustrate the ability and reliability of the mixture of the Laplace transform and the homotopy perturbation method. We have compared the analytical solution obtained with the available Laplace decomposition solution and the homotopy perturbation method of solution, which is found to be exactly the same. The result revealed that the combination of the Laplace transform and homotopy perturbation method is practically well- appropriate for use in such problems.