A solution algorithm for an inverse source problem for the kinetic equation
Ismet Golgeleyen, Muhammed Hasdemir
article (Uluslararası, Hakemli) | Yazar(lar): Ismet Golgeleyen, Muhammed Hasdemir | Yıl: 2022 | Dergi/Kurum: INTERNATIONAL JOURNAL OF MODERN PHYSICS C | İndeks: WOS.SCI | DOI: 10.1142/s0129183122501510 | Anahtar Kelimeler: Inverse problem, kinetic equation, finite difference method, stability, Lagrange interpolation —
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.