Two Algorithms For Solving A Kind Of Heat Conduction Equations
Cheng-Pu Tong 1, Xu-Ming Chen 11
Received 1982-9-4 Revised Online 2006-11-16
In this paper, a strategy is suggested for numerical solution of a kind of parabolio partial differential equations with nonlinear boundary conditions and discontinuous coefficients, which arise from practical engineering problems. First, a difference equation at the discontinuous point is established in which both the stability and the truncation error are consistent with the total difference equations. Then, on account of the fact that the coefficient matrix of the difference equations is trigiagonal and nonlinearity appears only in the first and the last equations, two algorithms are suggested: a mixed method combining the modified Gaussian elimination method with the successive recursion method, and a variant of the modified Gaussian elimination method. These algorithms are shown to be effective.