Analytical and numerical study of a class of nonlinear parabolic  moving boundary problems

Garshasbi, Morteza; Yaseen, Kulthom

doi:10.22055/jamm.2026.49388.2366

Analytical and numerical study of a class of nonlinear parabolic moving boundary problems

Document Type : Original Paper

Authors

Morteza Garshasbi

Kulthom Yaseen

School of Mathematics and Computer Science, Iran University of Science and Technology, Tehran, IRAN

10.22055/jamm.2026.49388.2366

Abstract

The main contribution of this article is the investigation of a parabolic problem with the moving boundary and nonlinear boundary conditions. Because of the non-linearity of the problem, it is important to put a lot of effort into providing efficient numerical schemes. For this purpose, a numerical approach based on the finite difference method with variable time steps is developed. First, based on the front-fixing approach, the problem is derived as a nonlinear fixed domain parabolic problem, and the uniqueness of the solution of the problem is proved. In sequence, a variable time step finite difference method is established to find the solution of the fixed domain problem. Finally, some numerical results are presented for two test problems to prove the ability and strength
of the numerical method

Keywords

Moving boundary problem

Nonlinear parabolic equations

Variable time step

Finite difference method

Uniqueness

Subjects