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《Journal of Natural Science of Hunan Normal University》 2017-04
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Studies on the Volterra Integral Equation with Linear Delay

ZHENG Wei-shan;Colloge of Mathematics and Statistics,Hanshan Normal University;  
This paper is concerned about the Volterra integral equation with linear delay.First we transfer the integral interval [0,T] into interval[-1,1]through the conversion of variables.Then we use the Gauss quadrature formula to get the approximate solutions.After that the Chebyshev spectral-collocation method is proposed to solve the equation.With the help of Gronwall inequality and some other lemmas,a rigorous error analysis is provided for the proposed method,which shows that the numerical error decay exponentially in the innity norm and the Chebyshev weighted Hilbert space norms.In the end,numerical example is given to confirm the theoretical results.
【Fund】: 国家自然科学基金资助项目(11626074);; 韩山师范学院创新强校项目(Z16027);韩山师范学院扶持项目(201404);; 中山大学广东省计算科学重点实验室开放基金资助项目(2016011)
【CateGory Index】: O175.5
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