COMBINING GENETIC ALGORITHM AND SINC-GALERKIN METHOD FOR SOLVING AN INVERSE DIFFUSION PROBLEM

A numerical approach combining the use of a genetic algorithm with the solution of the Sinc-Galerkin method is proposed for the determination of an unknown time-dependent diffusivity a(t) in an inverse diffusion problem (IDP). At the beginning of the numerical algorithm, Sinc-Galerkin method is employed to solve the direct diffusion problem. The present approach is to rearrange the matrix forms of the governing equations. Then, the genetic algorithm is adopted to find the solution of IDP. The genetic algorithm used in this work is not a classical genetic algorithm. Instead, the application of the genetic algorithm to this discrete-time optimal control problem is called a real-valued genetic algorithm(RVGA). Some numerical experiments confirm the utility of this algorithm as the results are in good agreement with the exact data. Results show that a reasonable estimation can be obtained by combining the genetic algorithm and Sinc-Galerkin method within a CPU with clock speed 2.7 GHz. Keywords: Inverse diffusion problem, genetic algorithm, Sinc-Galerkin method. AMS Subject Classification: 65M32, 35K05.