古振东, 孙丽英
古振东, 孙丽英. 一类弱奇性Volterra积分微分方程的级数展开数值解法[J]. 计算数学, 2017, 39(4): 351-362.
Gu Zhengdo, Sun Liying. SERIES EXPANSION METHOD FOR WEAKLY SINGULAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2017, 39(4): 351-362.
Gu Zhengdo, Sun Liying
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[1] Brewer D W, Powers R K. Parameter identification in a volterra equation with weakly singular kernel[J]. Journal of Integral Equations & Applications, 1990, 2(3):353-373.[2] Brunner H. Collocation methods for Volterra integral and related functional differential equations, vol. 15, Cambridge University Press, 2004.[3] Brunner H, Pedas A, Vainikko G. Piecewise polynomial collocation methods for linear volterra integro-differential equations with weakly singular kernels[J]. Siam Journal on Numerical Analysis, 39(3) (2001) 957-982.[4] Brunner H, Tang T. Polynomial spline collocation methods for the nonlinear basset equation[J]. Computers & Mathematics with Applications, 1989, 18(5):449-457.[5] Canuto C, Hussaini M Y, Quarteroni A, Zang T A. Spectral methods (fundamental in single domains), Springer, 2006.[6] Cao Y, Herdman T, Xu Y. A hybrid collocation method for volterra integral equations with weakly singular kernels[J]. Siam Journal on Numerical Analysis 2003, 41(1):364-381.[7] Cerezo G M. Solution representation and identication for singular neutral functional dierential equations, Virginia Tech.[8] Chen Y, Gu Z. Legendre spectral-collocation method for volterra integral differential equations with nonvanishing delay[J]. Communications in Applied Mathematics and Computational Science, 2013, 8(1):67-98.[9] Chen Y, Li X, Tang T. A note on jacobi spectral-collocation methods for weakly singular volterra integral equations with smooth solutions[J]. J. Comput. Math, 2013, 31:47-56.[10] Chen Y, Tang T. Spectral methods for weakly singular volterra integral equations with smooth solutions[J]. Journal of Computational and Applied Mathematics, 2009, 233(4):938-950.[11] Chen Y, Tang T. Convergence analysis of the jacobi spectral-collocation methods for volterra integral equations with a weakly singular kernel[J]. Mathematics of computation, 2010, 79(269):147-167.[12] Clements J C, Smith B R. Parameter estimation in a reaction-diffusion model for synaptic transmission at a neuromuscular junction[J]. Canad. appl. math. quart, 1996, 2:157-173.[13] Corduneanu A, Morosanu G. A linear integro-differential equation related to a problem from capillarity theory[J]. Communications on Applied Nonlinear Analysis, 1996, 3:51-60.[14] Gu Z. Multi-step chebyshev spectral collocation method for volterra integro-differential equations, Calcolo, 2015, 1-25.[15] Gu Z, Chen Y. Chebyshev spectral-collocation method for volterra integral equations[J]. Contemporary Mathematics, 2013, 586:163-170.[16] Gu Z, Chen Y. Chebyshev spectral-collocation method for a class of weakly singular volterra integral equations with proportional delay[J]. Journal of Numerical Mathematics, 2014, 22(4):311-342.[17] Gu Z, Chen Y. Legendre spectral-collocation method for volterra integral equations with nonvanishing delay[J]. Calcolo, 2014, 51(1):151-174.[18] Gu Z, Chen Y. Piecewise legendre spectral-collocation method for volterra integro-differential equations[J]. LMS Journal of Computation and Mathematics, 2015, 18(01):231-249.[19] Gu Z, Guo X, Sun D. Series expansion method for weakly singular volterra integral equations[J]. Applied Numerical Mathematics, 2016, 105:112-123.[20] Lubich C. Runge-kutta theory for volterra and abel integral equations of the second kind[J]. Mathematics of computation, 1983, 41(163):87-102.[21] Mustapha K, Brunner H, Mustapha H, Schotzau D. An hp-version discontinuous galerkin method for integro-differential equations of parabolic type[J]. Siam Journal on Numerical Analysis, 2011, 49(4):1369-1396.[22] Prosperetti A. A method for the solution of a class of singular volterra integro-differential equations[J]. Journal of Computational Physics, 1992, 46(3):462-468.[23] Tang T, Xu X, Cheng J. On spectral methods for volterra integral equations and the convergence analysis[J]. J. Comput. Math, 2008, 26(6):825-837.[24] Wei Y, Chen Y. Convergence analysis of the spectral methods for weakly singular volterra integrodifferential equations with smooth solutions[J]. Advances in Applied Mathematics & Mechanics, 2012, 4(1):1-20. |
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