Solution Of Poisson Equation By Trefftz Method
Free (open access)
E Kita, Y Ikeda & N Kamiya
This paper describes the application of the Trefftz method to the solution of the boundary value problems of the two-dimensional Poisson equation. The inhomogeneous term is approximated by polynomial functions and then, the solution for the Poisson equation is approximated by superposition of the Trefftz functions of the Laplace equation and the particular solutions related to the approximate inhomogeneous term. Unknown parameters are determined so that the solution satisfies the boundary conditions by means of the collocation method. The present scheme is applied to some examples in order to examine the numerical properties.