Product integration methods for solving a system of nonlinear Volterra integral equations

Journal of Computational and Applied Mathematics

Volumn 69, Issue 2, 1996, Pages 285-301

  Jumarhon, Bartur ^a   McKee, Sean ^b  

^a OXFORD BROOKES UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Product integration methods; Volterra equations

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; INTEGRATION; NONLINEAR EQUATIONS; NUMERICAL METHODS; PROBLEM SOLVING;

CONVERGENCE PROOFS; EULER SCHEMES; GLOBAL LIPSCHITZ CONDITION; NONLINEAR VOLTERRA INTEGRAL EQUATIONS; PRODUCT INTEGRATION;

INTEGRAL EQUATIONS;

EID: 0030146901     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/0377-0427(95)00041-0     Document Type: Article

References (18)

1. R.A. Badley, R.A.L. Drake, I.A. Shanks, A.M. Smith and P.R. Stephenson, Optical biosensors for immunoassays, the fluoresence capillary-fill device, Philos. Trans. Roy. Soc. London Ser. B 316 (1987) 143-160.
2. H. Brunner, Nonpolynomial spline collocation for Volterra equations with weakly singular kernels, SIAM J. Numer. Anal. 20 (1983) 1106-1119.
3. H. Brunner and P.J. van der Houwen, The Numerical Solution of Volterra Equations (North-Holland, Amsterdam, 1986).
4. N. Burgess, J. Dixon, S. Jones and M.L. Thoma, A reaction-diffusion study of a small cell, UCINA Report No. 86/2, Oxford University, 1986.
5. R.F. Cameron and S. McKee, Product integration methods for second-kind Abel integral equations, J. Comput. Appl. Math. 11 (1984) 1-10.
6. J.R. Cannon, The One-Dimensional Heat Equation (Addison-Wesley, Reading, MA, 1984).
7. T. Diogo, S. McKee and T. Tang, Collocation methods for second-kind Volterra integral equations with weakly singular kernels, Proc. Roy. Soc. Edinburgh Sect. A 124A (1994) 199-210.
8. J.A. Dixon, A nonlinear weakly singular Volterra integro-differential equation arising from a reaction-diffusion study of a small cell, J. Comput. Appl. Math. 18 (1987) 289-305.
9. P.P.B. Eggermont, On monotone Abel-Volterra integral equations on the half line, Numer. Math. 52 (1988) 65-79.
10. S. Jones, B. Jumarhon, S. McKee and J. Scott, A mathematical model of a biosensor, J. Engrg. Math., to appear.
11. B. Jumarhon and S. McKee, On the heat equation with nonlinear and nonlocal boundary conditions, J. Math. Anal. Appl. 190 (1995) 806-820.
12. P. Linz, Analytical and Numerical Methods for Volterra Equations (SIAM, Philadelphia, PA, 1985).
13. Ch. Lubich, Runge-Kutta theory for Volterra integral equations of the second kind, Math. Comp. 41 (1983) 87-102.
14. R.K. Miller and A. Feldstein, Smoothness of solutions of Volterra integral equations with weakly singular kernels, SIAM J. Math. Anal. 2 (1971) 242-258.
15. J. Norbury and A.M. Stuart, Singular nonlinear Volterra integral equations, Proc. Roy. Soc. Edinburgh Sect. A 106A (1987) 361-373.
16. J. Norbury and A.M. Stuart, Singular nonlinear Volterra integral equations, Proc. Roy. Soc. Edinburgh Sect. A 106A (1987) 375-384.
17. J. Ortega and W. Rheinbolt, Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, 1970).
18. H.J.J. te Riele, Collocation methods for weakly singular second kind Volterra integral equations with non-smooth solution, IMA J. Numer. Anal. 2 (1982) 437-449.