A kind of direct,implicit numerical scheme for unsteady nonlinear problems

摘要

In this paper,an unsteady nonlinear heat transfer problem governed by Hyperbolic Heat Conduction Equation(HHCE) with temperature-dependent heat conduction coefficient is used as an example to describe.the basic idesas of a direct,implicit numerical scheme for unsteady nonlinear problems in general.Different from traditional numerical approaches,this scheme can give accurate approximations of unsteady nonlinear problems duiscretizd in time domain in fully-implicit forms even by means of no iterations,Moreover,it possesses both numericall stability and calculation efficiency.Furthermore,this scheme can also provide us with a family of iterative formulas which include the traditional ones,say,the proposed numerical scheme also contains the traditional iterative methodology in logic.