Symbolic algorithm to solve initial value problems for partial differential equations

Abstract

In this paper, we present a new symbolic algorithm for finding the Green's function of a given initial value problem for linear partial differential equations of second order with constant coefficients. The proposed algorithm is also applicable for $n$-th order partial differential equations. We employ the integro-differential algebra to express the initial value problems and the Green's function. Some examples are presented to illustrate the proposed method and compared with other existing method. Link for implemented proposed algorithm in Maple is provided and sample computations are shown.

Keywords

• initial value problems
• partial differential equations
• symbolic method
• integro-differential algebra