Generalized Haar wavelet operational matrix method for solving hyperbolic heat conduction in thin surface layers

Abstract

It is remarkably known that one of the difficulties encountered in a numerical method for hyperbolic heat conduction equation is the numerical oscillation within the vicinity of jump discontinuities at the wave front. In this paper, a new method is proposed for solving non-Fourier heat conduction problem. It is a combination of finite difference and pseudospectral methods in which the time discretization is performed prior to spatial discretization. In this sense, a partial differential equation is reduced to an ordinary differential equation and solved implicitly with Haar wavelet basis. For the pseudospectral method, Haar wavelet expansion has been using considering its advantage of the absence of the Gibbs phenomenon at the jump continuities. We also derived generalized Haar operational matrix that extend usual domain (0,1] to (0,X]. The proposed method has been applied to one physical problem, namely thin surface layers. It is found that the proposed numerical results could suppress and eliminate the numerical oscillation in the vicinity jump and in good agreement with the analytic solution. In addition, our method is stable, convergent and easily coded. Numerical results demonstrate good performance of the method in term of accuracy and competitiveness compare to other numerical methods.