A fourth‐order compact finite difference scheme for solving an N‐carrier system with Neumann boundary conditions

In this study, we develop a fourth‐order compact finite difference scheme for solving a model of energy exchanges in a generalized N‐carrier system with heat sources and Neumann boundary conditions, which extends the concept of the well‐known parabolic two‐step model for microheat transfer. By using the matrix analysis, the compact finite difference numerical scheme is shown to be unconditionally stable. The accuracy of the solution obtained by the scheme is tested by a numerical example. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010