Variational Iteration Method for Solution of Two Dimension Fractional Diffusion Equations

Abstract

In the current research work we have introduced the Variational Iteration Method to obtain the Analytical Approximate Solution of the Two-Dimensional Diffusion Equation. We have used the initial value to determine the solution for various mathematical problems. This in turn has helped in accelerating the rapid convergence of the solution for the series. We have used the Variational Iteration method to solve the fractional-order diffusion equations for two dimensions. The series form solution for the fractional -order diffusion problem is obtained by the proposed method. We have effectively identified solutions for a wide range of physical and analytical problems during our research. Since we have demonstrated its effectiveness in finding the solutions for the fractional diffusion equations of two dimension, we can now say that VIM can be extremely helpful in tackling a wide range of engineering complexities. The Variation Iteration method has time and again proved to give exemplary result in terms of efficacy and simplicity. It has been proved superior and advantageous over the previously used analytical techniques Adomian Method, New Homotopy Perturbation Method, Homotopy [7.11,12] etc. The primary benefit of this strategy is that it allows us to achieve the desired result in a short amount of time. The obtained results are incredibly accurate and effective. We can also adapt this method for various other non-linear mathematical and scientific problems. We have tried to project mathematical results for various problems in the current research paper.