An Accurate and Stable Numerical Method for Solving a Micro Heat Transfer Model in a 1D N-Carrier System in Spherical Coordinates

We consider the generalized micro heat transfer model in a 1D microsphere with N-carriers and Neumann boundary condition in spherical coordinates, which can be applied to describe non-equilibrium heating in biological cells. An accurate and unconditionally stable Crank-Nicholson type of scheme is presented for solving the generalized model, where a new second-order accurate numerical scheme for the Neumann boundary condition is developed so that the overall truncation error is second-order. The present scheme is then tested by a numerical example. Results show that the numerical solution is much more accurate than that obtained based on the Crank-Nicholson scheme with the conventional method for the Neumann boundary condition. Furthermore, the convergence rate of the present scheme is about 1.8 with respect to the spatial variable, while the convergence rate of the Crank-Nicholson scheme with the conventional method for the Neumann boundary condition is only 1.0 with respect to the spatial variable.