An h-p version of the continuous Petrov-Galerkin method for Volterra delay-integro-differential equations

被引：7
作者：
Wang, Lina [1 ]
Yi, Lijun [1 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
来源：
ADVANCES IN COMPUTATIONAL MATHEMATICS | 2017年 / 43卷 / 06期
基金：
中国国家自然科学基金; 上海市自然科学基金;
关键词：
Volterra delay-integro-differential equations; h-p version; Continuous Petrov-Galerkin method; Error analysis; FINITE-ELEMENT-METHOD; INITIAL-VALUE PROBLEMS; SPECTRAL COLLOCATION METHODS; PRIORI ERROR ANALYSIS; RUNGE-KUTTA METHODS; INTEGRODIFFERENTIAL EQUATIONS; PARABOLIC PROBLEMS; PANTOGRAPH-TYPE; LEGENDRE; KERNELS;
D O I：
10.1007/s10444-017-9531-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider an h-p version of the continuous Petrov-Galerkin time stepping method for Volterra integro-differential equations with proportional delays. We derive a priori error bounds in the L (2)-, H (1)- and L (a)-norm that are explicit in the local time steps, the local approximation orders, and the local regularity of the exact solution. Numerical experiments are presented to illustrate the theoretical results.
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页码：1437 / 1467
页数：31
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