Quasi-reversibility and truncation methods to solve a Cauchy problem for the modified Helmholtz equation

Authors:
Hai-Hua Qin;Ting Wei
Affiliations:
School of Mathematics and Statistics, Lanzhou University, PR China;School of Mathematics and Statistics, Lanzhou University, PR China
Venue:
Mathematics and Computers in Simulation
Year:
2009

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Abstract

In this paper, the Cauchy problem for the modified Helmholtz equation in a rectangular domain is investigated. We use a quasi-reversibility method and a truncation method to solve it and present convergence estimates under two different a priori boundedness assumptions for the exact solution. The numerical results show that our proposed numerical methods work effectively.