分数阶多延迟抛物方程不同差分格式的分析

Discussion and analysis of different finite difference schemes for fractional multidelay parabolic equations

为获得分数阶多延迟抛物方程精确的解析表达式及其数值解,结合分数阶微积分的定义和数值方法,对分数阶多延迟抛物方程构造一类线性化的Crank-Nicolson差分格式和紧致差分格式.通过数值算例对差分格式的可解性、稳定性和收敛性进行验证.结果表明,该分数阶多延迟抛物方程的Crank-Nicolson差分格式和紧致差分格式具有良好的精确性和有效性.

In order to obtain the exact analytical expression and numerical solution of the fractional multidelay parabolic equation,a class of linearized Crank-Nicolson and compact difference schemes were constructed by combining the definition and numerical method of fractional calculus.Numerical examples are given to verify the resolvable,stability and convergence of the difference scheme.The results show that the Crank-Nicolson difference scheme and the compact difference scheme are accuracy and validity.