Time fractional of nonlinear heat-wave propagation in a rigid thermal conductor: Numerical treatment

Abstract

The objective of this article is to present the time-fractional nonlinear one-dimensional equations of damped heat wave propagation in a rigid thermal conductor slab and predicts the dependence of second sound velocity on temperature and heat flux. An efficient numerical method is presented for solving the proposed model. This method is a kind of non-standard finite difference weighted average. The numerical properties (stability, truncation error) of the proposed scheme are well investigated. The effectiveness of the numerical scheme is illustrated through test numerical examples.

Keywords

• Fractional nonlinear heat wave propagation equation
• Weighted average non-standard finite difference methods
• Kind of John von Neumann stability analysis
• Error estimates