zbMATH — the first resource for mathematics

Implicitly linear collocation methods for nonlinear Volterra equations. (English) Zbl 0761.65103
S. Kumar and I. H. Sloan [Math. Comput. 48, 585-593 (1987; Zbl 0616.65142)] introduced a new collocation-type method for Hammerstein integral equations. The author applies this method (which he calls implicitly linear collocation) to nonlinear Volterra integral and integro-differential equations and discusses the connection of the method with the iterated collocation method.
Reviewer: G.Vainikko (Tartu)

65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
Full Text: DOI
[1] Bellen, A.; Jackiewicz, Z.; Vermiglio, R.; Zennaro, M., Stability analysis of Runge-Kutta methods for Volterra integral equations of the second kind, IMA J. numer. anal., 10, 103-118, (1990) · Zbl 0686.65095
[2] Blom, J.G.; Brunner, H., The numerical solution of nonlinear Volterra integral equations of the second kind by collocation and iterated collocation methods, SIAM J. sci. statist. comput., 8, 806-830, (1987) · Zbl 0629.65144
[3] Brunner, H., Collocation methods for one-dimensional Fredholm and Volterra integral equations, (), 563-600
[4] H. Brunner, On discrete superconvergence properties of spline collocation methods for nonlinear Volterra integral equations, J. Comput. Math. (to appear). · Zbl 0758.65083
[5] Brunner, H., On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods, SIAM J. numer. anal., 27, (1990) · Zbl 0702.65104
[6] H. Brunner, On implicitly linear collocation methods for Hammerstein integral equations, J. Integral Equations Appl. (to appear). · Zbl 0749.65090
[7] Brunner, H.; van der Houwen, P.J., The numerical solution of Volterra equations, () · Zbl 0611.65092
[8] Ganesh, M.; Joshi, M.C., Discrete numerical solvability of Hammerstein integral equations of mixed type, J. integral equations appl., 2, 107-124, (1989) · Zbl 0708.65125
[9] Hairer, E.; Nørsett, S.P.; Wanner, G., Solving ordinary differential equations I: nonstiff problems, (1987), Springer Berlin · Zbl 0638.65058
[10] Krasnosel’skii, M.A.; Zabreiko, P.P., Geometrical methods of nonlinear analysis, (1984), Springer Berlin · Zbl 0546.47030
[11] Kumar, S., Superconvergence of a collocation-type method for Hammerstein equations, IMA J. numer. anal., 7, 313-325, (1987) · Zbl 0637.65140
[12] Kumar, S., A discrete collocation-type method for Hammerstein equations, SIAM J. numer. anal., 25, 328-341, (1988) · Zbl 0647.65090
[13] Kumar, S.; Sloan, I.H., A new collocation-type method for Hammerstein integral equations, Math. comp., 48, 585-593, (1987) · Zbl 0616.65142
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.