A High Accuracy Numerical Inversion Method in Solving the Sobolev Differential Equations

In the paper, by means of Laplace transform the Sobolev differential equations become to the elliptic differential equations, which can be solved by the fourth order finite difference equations in parallel. After getting the approximate solutions of the elliptic differential equations, we can achieve the numerical solutions with high accuracy for the Sobolev differential equations by using the Zakian inversion method. At last, we carry out one numerical experiment to indicate that the method in this paper is effective.