摘要
针对一类带初边值条件的分数阶反应-子扩散方程,构造了一种新的高阶隐式差分格式,其局部截断误差为O(τ1+γ+τγh4).并对格式的可解性做了分析.利用Fourier方法证明了格式的无条件稳定性.最后通过做数值算例去验证理论分析是有效可靠的.从所给的数值结果可以得出,该格式具有非常高的精度.
A kind of fractional reaction-subdiffusion equation with initial-boundary conditions is considered. A new high-order implicit difference scheme with local truncation error D（ τ^1＋γ,τγh^4） is constructed. The solvability of the scheme is analyzed. By means of Fourier method, the unconditional stability of the scheme is proved. Finally, a numerical example is given to verify the effectiveness of the theoretic analysis. The numerical results show that this scheme is of high accuracy.
出处
《湖南师范大学自然科学学报》
CAS
北大核心
2011年第6期6-11,共6页
Journal of Natural Science of Hunan Normal University
