Comparative analysis of new approximate analytical method and Mohand variational transform method for the solution of wave-like equations with variable coefficients

Abstract

In a current article, two novel analytical approaches are compared for analytical analysis of wave like equations with variable coefficients, which describe the evolution of stochastic phenomena. One is the New Approximate Analytical Method which based on Caputo–Riemann operator with simple decomposition procedure. This new method directly provides a fractional order series form solution which fastly converge to exact form solution for integer order. The second is Mohand Variational Iteration Transform Method which base on iteration procedure with Mohand Transform. The Mohand Variational Iteration Transform Method provides series form solution without using any decomposition, discretization, and He’s polynomial. The solution in series form converges directly to the exact solution for integer orders. The comparative analysis validates that Mohand Variational Iterative Method has less computational work and simple procedure without using any decomposition, discretization, and He’s polynomial procedure as compared to New Approximate Analytical Method.