Computational and Applied Mathematics

, Volume 35, Issue 1, pp 61–73

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

• M. Garshasbi
• H. Dastour
Article

## 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.

## Keywords

Ablation Stefan problem Inverse moving boundary Marching scheme Mollification

## Mathematics Subject Classification

65M32 65M06 65M12

## Notes

### Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments and suggestions which substantially improved the manuscript.

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