Accurate numerical method for solving dual-phase-lagging equation with temperature jump boundary condition in nano heat conduction

Dual-phase-lagging (DPL) equation with temperature jump boundary condition shows promising for analyzing nano heat conduction. For solving it, development of higher-order accurate and unconditionally stable (no restriction on the mesh ratio) numerical schemes is important. Because the grid size may be very small at nano-scale, using a higher-order accurate scheme will allow us to choose a relative coarse grid and obtain a reasonable solution. For this purpose, in this article we present a higher-order accurate and unconditionally stable compact finite difference scheme based on the ratio of relaxation times (0⩽B⩽1 and B>1). The method is illustrated by three numerical examples including a 2D case.