Two-dimensional multiple non-homogeneous harmonic equation and its boundary integral equations

摘要

The paper discusses 2-dimensional multiple non-homogeneous harmonic equation and its boundary integral equation, and gives recurrence formulae of fundamental solution. Under the assumption that non-homogeneous term is m-degree harmonic, the integral term in domain is shifted into boundary integral. Therefore the boundary integral equations are obtained that the integral in domain is not included, and the special solution can be expressed by boundary integrals. Furthermore, the error and convergence analysis are given by Taylor’s polynomial approximating non-homogeneous term f(x), and analytic expressions of boundary integral for 2-dimensional harmonic equation are given in local right-angle coordinate system.