摘要
This work is to provide general spectral and pseudo-spectral Jacobi-Petrov-Galerkin approaches for the second kind Volterra integro-differential equations.The Gauss-Legendre quadrature formula is used to approximate the integral operator and the inner product based on the Jacobi weight is implemented in the weak formulation in the numerical implementation.For some spectral and pseudo-spectral Jacobi-Petrov-Galerkin methods,a rigorous error analysis in both L2_(ω^(α,β))^(2),and L^(∞)norms is given provided that both the kernel function and the source function are sufficiently smooth.Numerical experiments validate the theoretical prediction.
基金
supported by the National Natural Science Foundation of China(10871066)
Project of Scientific Research Fund of Hunan Provincial Education Department(09K025)
Programme for New Century Excellent Talents in University(NCET-06-0712)
supported by the Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province
supported in part by Natural Science Foundation of Guizhou Province(LKS[2010]05).
