SOLUTION OF LINEAR-DIFFERENTIAL EQUATIONS BY THE METHOD OF DIVIDED DIFFERENCES

We introduce a new method for the solution of linear differential equa tions with constant coefficients. The solutions are obtained by the ap plication of a divided differences functional to a kernel function in two variables. For homogeneous equations the kernel is the product of a polynomial, which determines the initial values by exp(xt). For the inhomogeneous case the kernel is the convolution of the forcing functi on with exp(xt). If the forcing function is a quasi-polynomial then th ere is no need to compute convolutions. The method can also be applied to systems of equations and matrix differential equations. (C) 1995 A cademic Press, Inc.