A note on a positivity preserving hyperbolic NSFD scheme for heat transfer

Abstract

We construct a new nonstandard finite difference (NSFD) scheme for a hyperbolic partial differential equation (PDE) modelling heat transfer. This discretization satisfies a positivity condition for its solutions and is consistent in its general features with the experimental data. A brief discussion is also provided as to how the “additional” initial condition, , should be implemented on the computational grid. Further, we examine the details of the mathematical structure of the scheme and their implications for systems involving heat transfer.