Convergence analysis for fractional integral and differential equation with nonlinear delay
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Convergence analysis for fractional integral and differential equation with nonlinear delay
Acta Scientiarum Naturalium Universitatis SunYatseniVol. 57, Issue 1, Pages: 55-62(2018)
作者机构:
韩山师范学院数学与统计学院,广东,潮州,521041
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Published:2018,
Published Online:25 January 2018,
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ZHENG Weishan. Convergence analysis for fractional integral and differential equation with nonlinear delay. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(1):55-62(2018)
DOI:
ZHENG Weishan. Convergence analysis for fractional integral and differential equation with nonlinear delay. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(1):55-62(2018)DOI:
Convergence analysis for fractional integral and differential equation with nonlinear delay
The fractional integral and differential equation with nonlinear delay is studied with Jacobi spectralcollocation method. After proper linear transformation
an approximate solution and an approximate derivative of the solution are obtained by Gauss quadrature formula. By Jacobi collocation discretization
a rigorous error analysis is provided to show that the error of the approximate solution and the error of the approximate derivative both decay exponentially in the infinity norm and the weighted L
2
-norm.
关键词
Jacobi谱配置方法非线性延迟项分数阶导数微分积分方程高斯求积公式收敛分析
Keywords
Jacobi spectral-collocation methodnonlinear delayfractional derivativethe fractional integral and differential equationGauss quadrature formulaconvergence analysis