Solution of a singular integral equation by a split-interval method

International Journal of Numerical Analysis and Modeling

Volumn 4, Issue 1, 2007, Pages 63-73

  Diogo, Teresa ^a   Ford, Neville J ^b   Lima, Pedro M ^a   Thomas, Sophy M ^b  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b UNIVERSITY OF CHESTER   (United Kingdom)

Author keywords

Extrapolation; Numerical methods; Singular integral equation; Volterra equation

Indexed keywords

EID: 37548999467     PISSN: 17055105     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. H. Brunner. Collocation Methods for Volterra Integral and Related Functional Differential Equations, Cambridge University Press, 2004.
2. H. Brunner and P. J. van der Houwen. The Numerical Solution of Volterra Equations, North Holland, 1986.
3. C. Brezinski and M. Riedivo-Zaglia. Extrapolation Methods: Theory and Practice. North-Holland, Amsterdam, 1991.
4. T. Diogo, J.T. Edwards, N.J. Ford and S.M. Thomas. Numerical analysis of a singular integral equation, Appl. Math. Comp. 167 2005. p.372-382.
5. T. Diogo, J.M. Ford, N.J. Ford and P. Lima. Non-integrable resolvent kernels and qualitative behaviour for exact and approximate solutions to some convolution integral equations, submitted for publication.
6. T. Diogo, N. J. Ford, P. Lima and S. Valtchev. Numerical methods for a Volterra integral equation with non-smooth solutions, to appear in J. Comp. Appl. Math.
7. T. Diogo, S. McKee and T. Tang. A Hermite-type collocation method for the solution of an integral equation with certain weakly singular kernel, IMA J. Numer. Anal. 11 1991. p.595-605.
8. W. Han. Existence, uniqueness and smoothness results for second-kind Volterra equations with weakly singular kernels, J. Int. Eq. Appl. 6 1994. p.365-384.
9. P. Lima and T. Diogo. Numerical solution of a nonuniquely solvable Volterra integral equation using extrapolation methods, J. Comp. Appl. Math, 140 2002. p.537-557.
10. P. Lima and T. Diogo. An extrapolation method for a Volterra integral equation with weakly singular kernel, Appl. Numer. Math. 24 1997. p.131-148.
11. P. Linz. Analytical and Numerical Methods for Volterra Equations, SIAM. Philadephia. 1985.
12. T. Tang, S. McKee and T. Diogo, Product integration methods for an integral equation with a logarithmic singular kernel, Appl. Numer. Math. 9 1992. p.259-266.