Yunxia WEI
,
Yanping CHEN
. LEGENDRE SPECTRAL COLLOCATION METHOD FOR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION OF THE SECOND KIND[J]. Acta mathematica scientia, Series B, 2017
, 37(4)
: 1105
-1114
.
DOI: 10.1016/S0252-9602(17)30060-7
[1] Brunner H. Implicit Runge-Kutta methods of optimal order for Volterra integro-differential equations. Math Comp, 1984, 42:95-109
[2] Brunner H. Polynomial spline collocation methods for Volterra integro-differential equations with weakly singular kernels. IMA J Numer Anal, 1986, 6:221-239
[3] Brunner H, Pedas A, Vainikko G. Piecewise polynomial collocation methods for linear Volterra integrodifferential equations with weakly singular kernels. SIAM J Numer Anal, 2001, 39:957-982
[4] Brunner H, Schötzau D. hp-Discontinuous Galerkin time-stepping for Volterra integrodifferential equations. SIAM J Numer Anal, 2006, 44:224-245
[5] Chen Y, Li X, Tang T. A note on Jacobi spectral-collocation methods for weakly singular Volterra integral equations with smooth solutions. J Comput Math, 2013, 31:47-56
[6] Chen Y, Tang T. Spectral methods for weakly singular Volterra integral equations with smooth solutions. J Comput Appl Math, 2009, 233:938-950
[7] Chen Y, Tang T. Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel. Math Comp, 2010, 79:147-167
[8] Diogo T, Ma J T, Rebelo M. Fully discretized collocation methods for nonlinear singular Volterra integral equations. J Comput Appl Math, 2013, 247:84-101
[9] Goldfine A. Taylor series methods for the solution of Volterra integral and integro-differential equations. Math Comp, 1977, 31:691-707
[10] Ma S Q, Chang Q S. Strange attractors on pseudospectral solutions for dissipative Zakharov equations. Acta Math Sci, 2004, 24B:321-336
[11] Mastroianni G, Occorsio D. Optimal systems of nodes for Lagrange interpolation on bounded intervals. A survey. J Comput Appl Math, 2001, 134:25-341
[12] Shang Y D. The large time behavior of spectral approximation for a class of pseudoparabolic viscous diffusion equation. Acta Math Sci, 2007, 27B:153-168
[13] Shen J, Tang T, Wang L L. Spectral Methods Algorithms, Analysis and Applications. Springer, 2011
[14] Tang T, Xu X, Chen J. On spectral methods for Volterra integral equations and the convergence analysis. J Comput Math, 2008, 26:825-837
[15] Tarang M. Stability of the spline collocation method for second order Volterra integro-differential equations. Math Model Anal, 2004, 9:79-90
[16] Wei Y X, Chen Y. Convergence analysis of the legendre spectral collocation methods for second order Volterra integro-differential equations. Numer Math Theor Meth Appl, 2011, 4:339-358
[17] Wei Y X, Chen Y. Convergence analysis of the spectral methods for weakly singular Volterra integrodifferential equations with smooth solutions. Adv Appl Math Mech, 2012, 4:1-20
[18] Wei Y X, Chen Y. Legendre spectral collocation methods for pantograph Volterra delay-integro-differential equation. J Sci Comput, 2012, 53:672-688
[19] Wei Y X, Chen Y. A spectral method for neutral Volterra integro-differential equation with weakly singular kernel. Numer Math Theor Meth Appl, 2013, 6:424-446
[20] Wei Y X, Chen Y. Legendre spectral collocation method for neutral and high-order Volterra integrodifferential equation. Appl Numer Math, 2014, 81:15-29
[21] Yang Y, Chen Y, Huang Y. Convergence analysis of the Jacobi spectral-collocation method for fractional integro-differential equations. Acta Math Sci, 2014, 34B:673-690
[22] Yuan W, Tang T. The numerical analysis of implicit Runge-Kutta methods for a certain nonlinear integrodifferential equation. Math Comp, 1990, 54:155-168