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

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.