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

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Banei Siamak; Shanazari Kamal

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Journal Paper

Paper Information

Journal: Journal of Mathematical Modeling Year:2023 | Volume:11 | Issue:1 Page(s): 71-81

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Title

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

Author(s)

Banei Siamak | Shanazari Kamal | Issue Writer Certificate

Keywords

Non-homogeneous diffusion equations

meshfree method

method of fundamental solutions

time-dependent fundamental solutions

Abstract

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.

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