An adaptive wavelet collocation method for the optimal heat source problem

Abstract

PurposeThis paper aims to propose a new adaptive numerical method to find more accurate numerical solution for the heat source optimal control problem (OCP).Design/methodology/approachThe main aim of this paper is to present an adaptive collocation approach based on the interpolating wavelets to solve an OCP for finding optimal heat source, in a two-dimensional domain. This problem arises when the domain is heated by microwaves or by electromagnetic induction.FindingsThis paper shows that combination of interpolating wavelet basis and finite difference method makes an accurate structure to design adaptive algorithm for such problems which usually have non-smooth solution.Originality/valueThe proposed numerical technique is flexible for different OCP governed by a partial differential equation with box constraint over the control or the state function.