In this talk, we present a fully discrete method for solving the nonlinear convection-diffusion equations. The time discreteization is firstly advanced by a splitting method (Shi-Liang-Zhao-Zou, CICP14’) to derive a series of pure convection equations and diffusion equations. The new method is very efficient and the associated stiff matrices are positive definite and invariant along the time marching. These conclusions are demonstrated by several numerical experiments. This is a joint work with Y. Cao, J.Z. Li and H.B. Zheng.
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