The Method of Particular Solutions for Solving Inverse Problems of a Nonhomogeneous Convection-Diffusion Equation with Variable Coefficients

Abstract

A new version of the method of particular solutions (MPS) has been proposed for solving inverse problems for nonhomogeneous convection-diffusion equations with variable coefficients (IPCD). Coupled with the time discretization and MPS, the proposed method is a truly meshless method which requires neither domain or boundary discretization. Even though the final temperature is almost undetectable or is disturbed by significant noise, the proposed method can still recover the initial temperature very well. The effectiveness of the proposed inverse scheme using radial basis functions is demonstrated by several examples in 2-D and 3-D.

Acknowledgments

The third author acknowledges the support of the Distinguished Overseas Visiting Scholar Fellowship funded by the Minister of Education in China.

Supported by the National Natural Science Foundation of China [No. 11126126] and the Shandong Natural Science Foundation. The first author is a visiting professor in the Department of Mathematics, University of Southern Mississippi, Hattiesburg, Mississippi, USA.