Room: ACS 362C

Speaker: Dr. Nizomjon Jumaniyazov

Title: Numerical Solutions of Unsteady Fokker-Planck Type Kinetic Equations Using Finite Difference Methods

Abstract: The main goal of the work is to employ finite difference methods to solve the Fokker-Planck equation in general, with 4 variables: time, spatial, polar, and azimuthal variables. Finite difference method is used in two different ways: direct method and iterative method. Direct method is essentially based on Crank-Nicolson method containing both implicit and explicit schemes. Direct method consists of odd and even schemes with the meaning when the number of μ-nodes is odd and even respectively are applied. In what follows, to solve the problem by the iterative method, the odd scheme, which is more advantageous than the even one is used. The methods are compared in terms of computational time. In addition, the problem where the dependence on azimuthal angle θ is not neglected is considered. Using Fourier technique, the problem is divided into a collection of θ-independent problems whose absorption coefficients become singular, which requires to modify the odd scheme of the direct method. Finally, the methods employed, and results obtained will be applied to study time dependent Fokker-Planck Type Kinetic Equations.