一类求解非线性对流扩散方程的线性多步法

A second-order linear multi-step method for solving nonlinear convection-diffusion equations

研究一类非线性对流扩散方程,利用中心差商和线性多步法构造了一种新的在空间和时间上都具有二阶精度的差分格式,并利用Fourier分析和冻结系数方法分析了差分格式的稳定性,最后通过5种不同类型的数值算例验证了新方法求解非线性对流扩散方程的有效性.

A new scheme is developed for the nonlinear convection-diffusion equations in this paper.Based on the central difference and linear multi-step method,the proposed scheme achieves second-order accuracy in temporal and spatial variables.By using the Fourier method and freezing coefficient method,the stability of the proposed method is analyzed.Finally,numerical results illustrate the performance of the new scheme and support the theoretical properties of the estimator.