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 methods are of order h^(3/2) and h^(7/2) (his the increment size) depending on the finite difference approximations involved. CACM December, 1972 Moore, J. Robinson, P. parabolic equations, the Cauchy problem, method of successive approximations 5.17 CA721207 JB January 27, 1978 11:13 AM 2248 5 2248 2248 5 2248 2248 5 2248