A new approximation method for convection-diffusion equation by the fundamental solutions

Document Type : Research Article


Department of Mathematics, University of Kurdistan, Sanandaj, Iran


This paper develops a new numerical method of fundamental solutions for the non-homogeneeous convection-diffusion equations with time-dependent heat sources. A summation of the  fundamental solutions of  the diffusion operator is considered with time-dependent coefficients for the solution of the underlying problem. By the $\theta$-weight discretiztion for the  time derivative and selecting  the source points and the field points at each time level, the solutions of all time levels are  obtained. In addition, the stability of this approach is analyzed by considering $\theta=1$ in numerical results. This method is truly meshless and it is not necessary to discretize any part of  the domain or boundary.
As a result,  this method is easily applicable to higher dimensional  problems with  irregular domains.  In this work, we  consider  a non-homogeneous convection-diffusion equation (NCDE) in 2D with a regular domain and  present some  numerical results to show the effectiveness of the proposed method.