The truncation method for the Cauchy problem of the inhomogeneous Helmholtz equation

ABSTRACT

In this paper, the Cauchy problem of inhomogeneous Helmholtz equation is investigated. This problem is ill-posed and the truncation method is used to solve this inverse problem. Under the a priori and a posteriori parameter choice rules, the error estimates between the regularization solution and the exact solution is obtained, respectively. Numerical examples show that the truncation method works effectively.

KEYWORDS:

• Inhomogeneous Helmholtz equation
• ill-posed problem
• regularization method
• error estimate

AMS SUBJECT CLASSIFICATIONS:

• 35R25
• 47A52
• 35R30

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 [grant number 11561045], [grant number 11501272]; the Doctor Fund of Lan Zhou University of Technology.