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ABSTRACT
The Cauchy problem for the Helmholtz equation is considered. This problem is severely ill-posed, that is, the solution does not depend continuously on the data. To solve the problem numerically a mollification method is proposed. Convergence on error estimates between the exact solution and its approximation are obtained. Some numerical examples are given to show that the method works effectively.
Acknowledgments
The authors would like to thank the reviewers for their comments and suggestions that greatly helped to improve the readability of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
The project is supported by the National Natural Science Foundation of China [No. 11271187 and No. 11561045].