A mollified marching solution of an inverse ablation-type moving boundary problem

Abstract

This study investigates the application of marching scheme and mollification method to solve a one-dimensional inverse ablation-type moving boundary problem. The problem is considered with noisy data. A regularization method based on a marching scheme and discrete mollification approach is developed to solve the proposed problem and the stability and convergence of the numerical solution are proved. Some numerical experiments are presented to demonstrate the attractiveness and feasibility of the proposed approach. It is shown that the results are in good agreement with exact solutions.

Determination of unknown functions in a mathematical model of ductal carcinoma in situ

“…In sequence a numerical approach based on space marching method and mollification approach is developed to solve the problem (39)-(45). Space marching finite difference algorithms in conjunction with discrete mollification approach have been widely used to solve inverse parabolic problems in literature [19][20][21][22][23][24][25][26][27]. Using the space marching approach yields straightforward discretization of nonconstant coefficients and nonlinear problems.…”