An extrapolation method for a Volterra integral equation with weakly singular kernel

Applied Numerical Mathematics

Volumn 24, Issue 2-3, 1997, Pages 131-148

  Lima, Pedro ^a   Diogo, Teresa ^a  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

Asymptotic expansions; Euler's method; Richardson's extrapolation; Volterra integral equations

Indexed keywords

ASYMPTOTIC STABILITY; ERRORS; FUNCTIONS; INTERPOLATION; NUMERICAL METHODS;

ASYMPTOTIC ERROR EXPANSION; EULER METHOD; EXTRAPOLATION; RICHARDSON EXTRAPOLATION; VOLTERRA INTEGRAL EQUATION; WEAKLY SINGULAR KERNELS;

INTEGRAL EQUATIONS;

EID: 0031211649     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(97)00016-0     Document Type: Article

References (13)

1. M.A. Bartoshevich, On a class of Watson transforms, Dokl. Akad. Nauk USSR 220 (1975) 761-764.
2. C. Brezinski and M. Redivo-Zaglia, Extrapolation Methods: Theory and Practice (North-Holland, Amsterdam, 1991).
3. F. de Hoog and R. Weiss, Asymptotic expansions for product integration, Math. Comp. 27 (1973) 295-306.
4. T. Diogo and N.B. Franco, High order product integration methods for a Volterra integral equation with weakly singular kernel, to be submitted.
5. T. Diogo, S. McKee and T. Tang, A Hermite-type collation method for the solution of an integral equation with a certain weakly singular kernel, IMA J. Numer. Anal. 11 (1991) 595-605.
6. W. Han, Existence uniqueness and smoothness results for second-kind Volterra equations with weakly singular kernels, J. Integral Equations Appl. 6 (1994) 365-384.
7. W. Hock, An extrapolation method with step size control for nonlinear Volterra integral equations, Numer. Math. 38 (1981) 155-178.
8. W. Lamb, A spectral approach to an integral equation, Glasgow Math. J. 26 (1985) 85-89.
9. J.N. Lyness and B.W. Ninham, Numerical quadrature and asymptotic expansions, Math. Comp. 21 (1966) 162-178.
10. G.I. Marchuk and V.V. Shaidurov, Difference Methods and Their Extrapolations (Springer, Berlin, 1983).
11. P.G. Rooney, On an integral equation by Sub-Sizonenko, Glasgow Math. J. 24 (1983) 201-210.
12. J.A. Sub-Sizonenko, Inversion of an integral operator by the method of expansion with respect to orthogonal Watson operators, Siberian Math. J. 20 (1979) 318-321.
13. T. Tang, S. McKee and T. Diogo, Product integration methods for an integral equation with weakly singular kernel, Appl. Numer. Math. 9 (1992) 259-266.