A solution algorithm for an inverse source problem for the kinetic equation

İsmet Gölgeleyen and Muhammed Hasdemir ()
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İsmet Gölgeleyen: Department of Mathematics, Faculty of Arts and Sciences, Zonguldak Bülent Ecevit University, Zonguldak 67100, Turkey
Muhammed Hasdemir: Department of Mathematics, Faculty of Arts and Sciences, Zonguldak Bülent Ecevit University, Zonguldak 67100, Turkey

International Journal of Modern Physics C (IJMPC), 2022, vol. 33, issue 11, 1-18

Abstract: In this work, we deal with an inverse source problem for the kinetic equation. We obtain numerical solution of the problem by using a hybrid method which is composed of finite difference approximation and Lagrange’s polynomial interpolation. We present necessary conditions for the stability of the finite difference scheme by the Von Neumann method. Finally, we test the proposed method by performing several numerical experiments. We conclude that the relative error in reconstruction of the unknown functions is sufficiently small.

Keywords: Inverse problem; kinetic equation; finite difference method; stability; Lagrange interpolation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0129183122501510

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