Runge-kutta theory for volterra and abel integral equations of the second kind

Mathematics of Computation

Volumn 41, Issue 163, 1983, Pages 87-102

  Lubich, Ch ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84962571892     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1983-0701626-6     Document Type: Article

References (14)

1. M. Abramowitz & I. A. Stegun (Editors), Handbook of Mathematical Functions, Dover. New York, 1964.
2. U. an der Heiden, Analysis of Neural Networks, Lecture Notes in Biomathematics, Vol. 35, Springer-Verlag, Berlin. Heidelberg, New York, 1980.
3. H. Brunner, E. Hairer & S. P. Norsett, "Runge-Kutta theory for Volterra integral equations of the second kind," Math. Comp., v. 39, 1982, pp. 147-163.
4. H. Brunner & S. P. Norsett, "Superconvergence of collocation methods for Volterra and Abel integral equations of the second kind," Numer. Math. v. 36, 1981, pp. 347-358.
5. H. BRUNNER& H. J. J. teriele, Volterra-Type Integral Equations of the Second Kind with Non-Smooth Solutions: High-Order Methods Based on Collocation Techniques, Report NW 118, Mathematisch Centrum, Amsterdam, 1982.
6. J. C. Butcher, "Implicit Runge-Kutta and related methods," Modern Numerical Methods for Ordinary Differential Equations (G. Hall and J. M. Watt, eds.). Clarendon Press, Oxford, 1976. pp. 136-151.
7. F. dehoog & R. Weiss, "High order methods for a class of Volterra integral equations with weakly singular kernels," SIAM J. Numer. Anal., v. 11. 1974, pp. 1166-1180.
8. E. Hairer & G. Wanner, "On the Butcher group and general multi-value methods," Computing, v. 13, 1974. pp. 1-15.
9. R. K. Miller & A. Feldstein, "Smoothness of solutions of Volterra integral equations with weakly singular kernels," SIAM J. Math. Anal., v. 2, 1971, pp. 242-258.
10. S. P. Norsett & G. Wanner, "The real-pole sandwich for rational approximations and oscillation equations," BIT. v. 19. 1979, pp. 79-94.
11. H. Oules, "Resolution numérique d'une équation intégrale singulière," Rev. Française Traitement Information, v. 7, 1964, pp. 117-124.
12. P. Pouzet, "Etude en vue de leur traitement numérique des équations intégrales de type Volterra," Rev. Française Traitement Information, v. 6, 1963, pp. 79-112.
13. H. J. J. TE Riele, Collocation Methods for Weakly Singular Second Kind Volterra Integral Equations with Non-Smooth Solution, Report NW 115, Mathematisch Centrum, Amsterdam, 1981.
14. B. Ferebee, The Tangent Approximation to One-Sided Brownian Exit Densities, Univ. Heidelberg, SFB 123, Techn. Rep. Nr. 138, 1981.