Determination of a time-dependent source term using local meshless method

Volume 6, Issue 6, December 2021     |     PP. 101-113      |     PDF (798 K)    |     Pub. Date: December 28, 2021
DOI: 10.54647/mathematics11265    74 Downloads     5789 Views  

Author(s)

Baiyu Wang, College of Computer Engineering and Applied Mathematics, Changsha University, China
Wei Liu, College of Computer Engineering and Applied Mathematics, Changsha University, China

Abstract
For the past few years, the meshless method has played a great advantage in solving partial differential equations. In this paper, a local meshless method based on moving least square and local radial basis functions is used to solve the inverse problem of heat conduction equation. The inverse problem is determination of a source term, and the unknown source term is time dependent. Numerical experiments are given to demonstrate the accuracy, effectiveness and feasibility of this method.

Keywords
Local meshless method, Inverse problem, Heat equation, Source term

Cite this paper
Baiyu Wang, Wei Liu, Determination of a time-dependent source term using local meshless method , SCIREA Journal of Mathematics. Volume 6, Issue 6, December 2021 | PP. 101-113. 10.54647/mathematics11265

References

[ 1 ] LIU Z.H., WANG B.Y., Coefficient Identification in Parabolic Equations. Applied Mathematics and Computation , 209,379-390,2009.
[ 2 ] SAADATMANDI A., DEHGHAN M., Computation of Two-Dependent Coefficients in a Parabolic Partial Differential Equation Subject to Additional Specifications. International Journal of Computer Mathematics , 87,997-1008,2010.
[ 3 ] HUSSEIN M. S., LESNIC D., Simultaneous Determination of Time and Space-Dependent Coefficients in a Parabolic Equation. Communications in Nonlinear Science and Numerical Simulation , 33,194-217,2016.
[ 4 ] FATULLAYEV A. G., Numerical Solution of the Inverse Problem of Determining an Unknown Source Term in a Heat Equation. Mathematics and Computers in Simulation , 58,247-253,2002.
[ 5 ] LE DINH LONG, ZHOU Y., TRAN THANA BINH and NGUYEN CAN., A Mollification Regularization Method for the Inverse Source Problem for a Time Fractional Diffusion Equation. Mathematics , 7, 1048; doi:10.3390/math7111048,2019.
[ 6 ] MUHAMMAD ALI, SARA AZIZ, SALMAN A MALIK., Inverse source problems for a space-time fractional differential equation. Inverse Problems in Science and Engineering , 28(1),47-68,2019.
[ 7 ] WANG B.Y., Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem. Abstract and Applied Analysis , Article ID 686020, 12 pages,2014.
[ 8 ] YAN L., FU C.L., YANG F.L., The method of fundamental solutions for the inverse heat source problem. Engineering Analysis with Boundary Elements , 32,216-222,2008.
[ 9 ] AMIRFAKHRIAN M., ARGHAND M., KANSA E. J., A new approximate method for an inverse time-dependent heat source problem using fundamental solutions and RBFs. Engineering Analysis with Boundary Elements , 64,278-289,2016.
[ 10 ] FARCAS A., LESNIC D., The Boundary-Element Method for the Determination of a Heat Source Dependent on One Variable. Journal of Engineering Mathematics , 54,375-388,2006.
[ 11 ] WANG B.Y., A Local Meshless Method Based on Moving Least Squares and Local Radial Basis Functions. Engineering Analysis with Boundary Elements , 50,395-401,2015.
[ 12 ] LIU W., WANG B.Y., A local meshless method for two classes of parabolic inverse problems. Journal of Applied Mathematics and Physics , 6,968-978,2018.