一类时滞分数阶Volterra微积分方程组的严格误差分析

Sharp error estimate for fractional Volterra integro-differential equations with delay

采用谱配置方法分析带一般时滞项的分数阶Volterra微积分方程.通过严格的误差分析证明了近似解的误差和近似分数阶导数的误差在L^(∞)和L_(ω^(-μ,-μ))^(2)模意义下呈指数衰减.最后用数值例子来验证理论分析的正确性.

Spectral methods are developed for solving fractional differential equations with vanishing delay numerically.Sharp error estimates are carried out,which indicates that the error of solution and the error of exact fractional derivative decay exponentially in both L^(∞)and L_(ω^(-μ,-μ))^(2).In the end,a numerical example is presented to confirm our theoretical findings.