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

Author

Listed:
  • Ä°smet 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)

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.

Suggested Citation

  • Ä°smet Gölgeleyen & Muhammed Hasdemir, 2022. "A solution algorithm for an inverse source problem for the kinetic equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 33(11), pages 1-18, November.
    • Handle: RePEc:wsi:ijmpcx:v:33:y:2022:i:11:n:s0129183122501510
    DOI: 10.1142/S0129183122501510
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