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

Abstract

A numerical approach combining the use of a genetic algorithm with thesolution of the Sinc-Galerkin method is proposed for the determination of an unknowntime-dependent diffusivity a(t) in an inverse diffusion problem (IDP). At the beginning ofthe numerical algorithm, Sinc-Galerkin method is employed to solve the direct diffusionproblem. 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 geneticalgorithm 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 areal-valued genetic algorithm(RVGA). Some numerical experiments confirm the utilityof this algorithm as the results are in good agreement with the exact data. Results showthat a reasonable estimation can be obtained by combining the genetic algorithm andSinc-Galerkin method within a CPU with clock speed 2.7 GHz.