摘要
考虑了变系数分数阶反应-扩散方程,将一阶的时间偏导数和二阶的空间偏导数分别用Caputo分数阶导数和Riemann-Liouville分数阶导数替换,利用L1算法和G算法对方程的变系数分数阶导数进行适当的离散,给出了该方程的一种计算有效的隐式差分格式,并证明了这个差分格式是无条件稳定和无条件收敛的,且具有o(τ+h)收敛阶.最后用数值例子说明差分格式是有效的.
A fractional reaction-dispersion equation with variable coefficients is considered which the first-order time derivative and the second-order space derivative is replacing by Caputo fractional derivative and Riemann-Liouville derivative respectively, and an implicit difference scheme is presented by using the algorithm of L1 and G to discrete the variable coefficients fractional derivative efficaciously. It is showed that the scheme is unconditional stable and convergence respectively, the convergence order of the scheme is o（τ＋h）. Finally, a numerical example demonstrates the difference method is effective.
出处
《沈阳大学学报（自然科学版）》
CAS
2014年第1期76-80,共5页
Journal of Shenyang University：Natural Science
基金
国家自然科学基金资助项目(10671132
60673192)
攀枝花学院校级科研项目(2013YB05)
关键词
变系数
反应一扩散方程
隐式差分
稳定性
收敛性
variable coefficients
reaction-dispersion equation
implicit difference
stability
convergence
