The Picard contraction mapping method for the parameter inversion of reaction-diffusion systems

Authors:
Xiaoyan Deng;Bangju Wang;Guangqing Long
Affiliations:
College of Basic Sciences, Huazhong Agriculture University, Wuhan, 430070, PR China;College of Basic Sciences, Huazhong Agriculture University, Wuhan, 430070, PR China;Department of Mathematics, Guangxi Normal College, Nanning 530001, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

An inverse problem is to determine unknown causes based on observation of their effects. Such problems often arise in scientific research and engineering practice. In this paper we present a parameter inversion method for a class of reaction-diffusion systems by the use of the Picard contraction mapping. We firstly establish an approximate differential equation model which corresponds to the given reaction-diffusion system, and discuss the contractivity of the Picard mapping associated with the approximate model. Then we provide an algorithm for recovering parameters of the reaction-diffusion system based on the Collage theorem. Numerical tests show that the proposed method is efficient.