A New Method for the Solution of the Cauchy Problem for Parabolic Equations.

An integral equation representation is given for parabolic 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 h^3/2 and h^7/2 (h is the increment size) depending on the finite difference approximations involved. [ABSTRACT FROM AUTHOR]