A Fourth-Order Modified Method for the Cauchy Problem of the Modified Helmholtz Equation

作者：Shi R; Wei T^*; Qin H H

来源：Numerical Mathematics: Theory, Methods and Applications , 2009, 2(3): 326-340.

DOI：10.4208/nmtma.2009.m88032

• Cauchy problem for the modified Helmholtz equation
• ill-posed problem
• fourth-order modified method

This paper is concerned with the Cauchy problem for the modified Helmholtz equation in an infinite strip domain 0 < x <= 1, y is an element of R. The Cauchy data at x = 0 is given and the solution is then sought for the interval 0 < x <= 1. This problem is highly ill-posed and the solution (if it exists) does not depend continuously on the given data. In this paper, we propose a fourth-order modified method to solve the Cauchy problem. Convergence estimates are presented under the suitable choices of regularization parameters and the a priori assumption on the bounds of the exact solution. Numerical implementation is considered and the numerical examples show that our proposed method is effective and stable.

• 出版日期2009-8
• 单位兰州大学