Full entry |
PDF
(0.3 MB)
Feedback

Volterra integral equations; Galerkin methods; convergence and superconvergence; interpolation post-processing; iterative correction; a posteriori error estimators

References:

[1] K. Atkinson, J. Flores: **The discrete collocation method for nonlinear integral equations**. IMA J. Numer. Anal. 13 (1993), 195–213. DOI 10.1093/imanum/13.2.195 | MR 1210822

[2] H. Brunner: **Iterated collocation methods and their discretization for Volterra integral equations**. SIAM J. Numer. Anal. 21 (1984), 1132–1145. DOI 10.1137/0721070 | MR 0765511

[3] H. Brunner: **The approximate solution of Volterra equations with nonsmooth solutions**. Utilitas Math. 27 (1985), 57–95. MR 0804372 | Zbl 0563.65077

[4] H. Brunner: **A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equations**. J. Comput. Appl. Math. 8 (1982), 213–229. DOI 10.1016/0771-050X(82)90044-4 | MR 0682889 | Zbl 0485.65087

[5] H. Brunner, P. J. Van der Houwen: **The Numerical Solution of Volterra Equations. CWI Monographs, Vol. 3**. North-Holland, Amsterdam, 1986. MR 0871871

[6] H. Brunner, Q. Lin, N. Yan: **The iterative correction method for Volterra integral equations**. BIT 36:2 (1996), 221–228. DOI 10.1007/BF01731980 | MR 1432245

[7] H. Brunner, Y. Lin, S. Zhang: **Higher accuracy methods for second-kind Volterra integral equations based on asymptotic expansions of iterated Galerkin methods**. J. Integ. Eqs. Appl 10, 4 (1998), 375–396. MR 1669667

[8] H. Brunner, A. Pedas, G. Vainikko: **The piecewise polynomial collocation methods for nonlinear weakly singular Volterra equations**. Research Reports A 392, Institute of Mathematics, Helsinki University of Technology, 1997.

[9] H. Brunner, N. Yan: **On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations**. J. Comput. Appl. Math. 67 (1996), 187–189. DOI 10.1016/0377-0427(96)00012-X | MR 1388148

[10] Q. Hu: **Stieltjes derivatives and $\beta $-polynomial spline collocation for Volterra integro-differential equations with singularities**. SIAM J. Numer. Anal. 33, 1 (1996), 208–220. DOI 10.1137/0733012 | MR 1377251

[11] M. Křížek, P. Neittaanmäki: **Finite Element Approximation of Variational Problems and Applications**. Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Essex, 1990. MR 1066462

[12] Q. Lin, I.H. Sloan, R. Xie: **Extrapolation of the iterated-collocation method for integral equations of the second kind**. SIAM J. Numer. Anal. 27, 6 (1990), 1535–1541. DOI 10.1137/0727090 | MR 1080337

[13] Q. Lin, S. Zhang: **An immediate analysis for global superconvergence for integrodifferential equations**. Appl. Math. 1 (1997), 1–21. DOI 10.1023/A:1022264125558 | MR 1426677

[14] Q. Lin, S. Zhang, N. Yan: **Methods for improving approximate accuracy for hyperbolic integrodifferential equations**. Systems Sci. Math. Sci., 10, 3 (1997), 282–288. MR 1469188

[15] Q. Lin, S. Zhang, N. Yan: **An acceleration method for integral equations by using interpolation post-processing**. Advances in Comput. Math. 9 (1998), 117–129. DOI 10.1023/A:1018925103993 | MR 1662762

[16] I. H. Sloan: **Superconvergence**. Numerical Solution of Integral Equations, M. A. Golberg (ed.), Plenum Press, New York, 1990, pp. 35–70. MR 1067150 | Zbl 0759.65091