In this paper, a new method for numerically solving nonlinear convection-dominated diffusion problems is devised and analysed. The discrete time approximations with time stepping along charactcristics are cstablished ...In this paper, a new method for numerically solving nonlinear convection-dominated diffusion problems is devised and analysed. The discrete time approximations with time stepping along charactcristics are cstablished and solved in spaces posscssing reproducing kernel functions. At each time step, the exact solution of the approximate problem is given by explicit expression. The computational advantage of this method is that the schemes are absolutely stable, and are explicitly solvable as well. The stability and error estimates are derived. Some numerical results are given.展开更多
基金Project supported by the Doctoral Point Foundation of State Education Commission of China
文摘In this paper, a new method for numerically solving nonlinear convection-dominated diffusion problems is devised and analysed. The discrete time approximations with time stepping along charactcristics are cstablished and solved in spaces posscssing reproducing kernel functions. At each time step, the exact solution of the approximate problem is given by explicit expression. The computational advantage of this method is that the schemes are absolutely stable, and are explicitly solvable as well. The stability and error estimates are derived. Some numerical results are given.
