A New Numerical Algorithm for Solving Fundamental Solutions

Abstract

In this paper the new numerical algorithm for solving fundamental solutions i.e. Green’s functions is proposed. By direct discreting after integrating differential equation, it is possible for one to get the numerical solutions of Green’s functions satisfying the governing differential equation. Owing to avoidance of the integral transform in the method proposed in this paper, it is natural that there exists no ill-possed mathematical problem of the inverse integral transform. As a result of this not only a great quantity of calculation can be reduced but also the accuracy and steadiness of calculation improved. It is suitable for various classes of differential equation and varieties of boundary condition. The paper gives a numerical result. The new algorithm is fully proved to be available in practical applicâtion. It is worth pointing out as Green’s functions are expressed in this paper in an inverse matrix form, it is not only fairly easy to be accepted and mastered by engineers and technicians, but also convenient to be realized on computers.