Transient heat conduction by different versions of the Method of Fundamental Solutions - a comparison study

Abstract

The computational accuracy of three versions of the method of fundamental solutions (MFS) is compared. The first version of MFS is based on the Laplace transformation of the governing differential equations and of the boundary conditions. The second version of MFS is based on the fundamental solution of the governing differential equation and discretization in time. The third method approximates the temperature time derivative by finite difference scheme. As the test problems the 2D boundary-initial-value problems (2D_BIVP) in square rectangular region Ω with known exact solutions are considered. Our numerical experiments show that all discussed methods achieve relatively accurate approximate solution but the third one offers less computational complexity and better efficiency.