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

The main contribution of this article is the investigation of a parabolicproblem 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 differencemethod 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

کلیدواژه ها:

moving boundary problem ، Nonlinear parabolic equations ، variable time step ، Finite difference method ، uniqueness