A NEW APPLICATION OF USING HOMOTOPY ANALYSIS METHOD FOR SOLVING STOCHASTIC QUADRATIC NONLINEAR DIFFUSION EQUATION

The homotopy analysis method (HAM) is applied to obtain some approximate orders of mean and variance for the solution process quadratic nonlinear diffusion equation under stochastic non homogeneity. The scheme shows importance of choice of convergence control parameter  to guarantee the convergence of the solution. The method provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software such as Mathematica. The method of solution is illustrated through figures, comparisons among different methods and some parametric studies have been done to show accuracy of the presented method.