An Implicit Approximation for the Caputo Fractional Reaction-Dispersion Equation

分数阶微分方程在许多应用科学上比整数阶微分方程更能准确地模拟自然现象.本文考虑分数阶反应-扩散方程.将一阶的时间偏导数用Caputo分数阶导数替换,并给出了一个隐式的差分格式.利用能量方法给出此差分格式的稳定性与收敛性证明,最后用数值例子说明差分格式是有效的.Fractional differential equations can more correctly simulate many phenomena contrasting with integer differential equations in lost of applied science.In this paper,a time-fractional reaction-dispersion equation was considered which the first order derivative was replaced by a Caputo fractional derivative,and an implicit difference scheme was given.Stability and convergence were proved by using energy method.A numerical example demonstrates the difference method is effective.国家自然科学基金(10271098)资