A Fourth-Order Compact Finite Difference Scheme for Solving an N-Carrier System with Neumann Boundary Conditions

作者：Dai Weizhong^*; Tzou Da Yu

来源：Numerical Methods for Partial Differential Equations, 2010, 26(2): 274-289.

DOI：10.1002/num.20427

• compact finite difference scheme
• energy exchange
• N-carrier system
• Neumann boundary condition
• matrix analysis
• stability

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.

• 出版日期2010-3