发展型方程的快速Legendre谱τ逼近

Fast Legendre Spectral Tau Approximation for Evolutionary Problems

以发展型模型方程为背景,建立了半离散和全离散的Legendre谱τ格式,并用反向递推法和奇偶分解法建立了Legendre谱τ方法的快速算法,在每一时间层上,其运算量仅为O(N).运用离散能量法严格证明了全离散格式在时空方向的收敛阶分别为τ2和N1-m.数值结果显示了算法的有效性.

The linear evolutionary equation was considered. The semi and fully discrete Legendre spectral Tau schemes were proposed. The corresponding algorithms were achieved by using the Galerkin differential recurrence formula in space which leads to a system with sparse matrix. The complexity of the algorithms are O(N) on each time level. It was strictly proved that the numerical solution possesses the second order in time and higher order in space. The algorithms are supported by the numerical results efficiently.