Numerical simulations for initial value inversion problem in a two-dimensional degenerate parabolic equation

Abstract

In this paper, we study the inverse problem of identifying the initial value of a two-dimensional degenerate parabolic equation, which often appears in the fields of engineering, physics, and computer image processing. Firstly, the difference scheme of forward problem is established by using the finite volume method. Then stability and convergence of the difference equations are proved rigorously. Finally, the Landweber iteration and conjugate gradient method are used to solve the inverse problem, and some typical numerical examples are shown to verify the validity of our iterative algorithm. Numerical results show that the algorithm is stable and efficient.

Keywords

• initial value inversion problem
• degenerate parabolic equation
• difference scheme
• stability
• numerical simulation