Abstract
This paper describes the Trefftz solution of the boudnary value problem governed with the three-dimensional Poisson equation. The inhomogeneous term of the governing equation is approximated with the polynomial function in the orthogonal coordinates in order to derive the particular solution related to the term. The solution of the problem is approximated with the superposition of the homogeneous solution of Laplace equation and the derived particular solutions with unknowns. Unknown parameters are determined so that the approximate function satisfies the boundary conditions by means of the collocation method.
