Mixed Transform Iterative Method for Solving Wave Like Equations

Abstract

    In this article, a hybrid method that combines Aboodh transform, variational iteration method, and the homotopy perturbation method is presented for approximate the solution of important partial differential equations that describe wave like differential equations in one, two and three dimensions. The suggested method utilizes only the initial conditions to provide an analytical solution, in contrast to the method of separation of variables, that also requires boundary conditions. This method makes use of the Aboodh's transform advantageous on the Lagrange multiplier computation, hence there is no need to use the convolution theorem or any integration in a recurrence relation for the process of finding it. The obtained exact solutions are found as a convergent series with components that are simple to compute. In addition, the method needs no any assumptions that change the problem's physical nature, such as those that involve discretization, linearization, or minor factors compared to certain other techniques. Some examples are given to show how efficient and useful the method is.