Reconstruction robin boundary condition in the heat conduction inverse problem of fractional order

Abstract

This paper describes a parallel algorithm for reconstruction the boundary condition for the heat conduction equation with derivative of fractional order with respect to the time. The heat transfer coefficient, occurring in the boundary condition of the third kind, was reconstructed. Additional information for the considered inverse problem is given by the temperature measurements at selected points of the domain. The direct problem was solved by using the implicit finite difference method. To minimize functional defining the error of approximate solution parallel Ant Colony Optimization algorithm (ACO) was used. Calculations have been performed in parallel way (multi-threaded). The paper presents examples to illustrate the accuracy and stability of the presented algorithm.