Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method

Abstract

In this study, the solutions of random partial differential equations are examined. The parameters and the initial conditions of the random component partial differential equations are investigated with Beta distribution. A few examples are given to illustrate the efficiency of the solutions obtained with the random Differential Transformation Method (rDTM). Functions for the expected values and the variances of the approximate analytical solutions of the random equations are obtained. Random Differential Transformation Method is applied to examine the solutions of these partial differential equations and MAPLE software is used for the finding the solutions and drawing the figures. Also the Laplace- Pade Method is used to improve the convergence of the solutions. The results for the random component partial differential equations with Beta distribution are analysed to investigate effects of this distribution on the results. Random characteristics of the equations are compared with the results of the deterministic partial differential equations. The efficiency of the method for the random component partial differential equations is investigated by comparing the formulas for the expected values and variances with results from the simulations of the random equations.