A new method for the solution of the Cauchy problem for parabolic equations

partial differential equations. When the equations are defined in unbounded domains, as in the initial value (Cauchy) problem, the solution of the integral equation by the method of successive approximation has inherent advantages over other methods. Error bounds for the method are of order h3/2 and h7/2 (h is the increment size) depending on the finite difference approximations involved.