Theory and Application of the Generalized Integral Representation Method (GIRM) in Advection Diffusion Problem

Abstract

The integral representation is developed for linear initial and boundary value problems. The fundamental solution is defined by the linear differential equation with constant coefficients and plays a key role in obtaining the integral representation. This becomes a very strong constraint in developing the theory to nonlinear problems. In the present paper, an innovative generalization of the integral representation or generalized integral representation is proposed. The numerical examples are given to verify the theory.