A new method of fundamental solutions for time-dependent non-homogeneous heat source problems

We present a method of fundamental solutions for the non-homogeneous diffusion equations with time-dependent heat sources. In the classical method of fundamental solution, rst, the solution of the homogeneous equation is expressed as a combination of the time-dependent fundamental solution and then an approximation of the paricular solution is used to obtain the solution of the main equation. In this work, the solution of the non-homogeneous problem is assumed as a combination of the fundamental solutions of the diffusion operator with time-dependent coefficients. The suggested method is truely meshless and does not use any sort of discretization and nodal connectivities. Some 2-D and 3-D numerical exampls are presented toshow the effectiveness of the new method.

کلیدواژه ها:

Non-homogeneous diffusion equations ، Meshfree method ، Method of fundamental solutions ، Time-dependent fundamental solutions.