Runge-Kutta Theory for Volterra and Abel Integral Equations of the Second Kind
- 1 July 1983
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 41 (163), 87-102
- https://doi.org/10.2307/2007768
Abstract
The present paper develops the local theory of general Runge-Kutta methods for a broad class of weakly singular and regular Volterra integral equations of the second kind. Further, the smoothness properties of the exact solutions of such equations are investigated.Keywords
This publication has 8 references indexed in Scilit:
- Runge-Kutta Theory for Volterra Integral Equations of the Second KindMathematics of Computation, 1982
- The tangent approximation to one-sided Brownian exit densitiesProbability Theory and Related Fields, 1982
- Superconvergence of collocation methods for Volterra and Abel integral equations of the second kindNumerische Mathematik, 1981
- Analysis of Neural NetworksPublished by Springer Science and Business Media LLC ,1980
- The real-pole sandwich for rational approximations and oscillation equationsBIT Numerical Mathematics, 1979
- High Order Methods for a Class of Volterra Integral Equations with Weakly Singular KernelsSIAM Journal on Numerical Analysis, 1974
- On the Butcher group and general multi-value methodsComputing, 1974
- Smoothness of Solutions of Volterra Integral Equations with Weakly Singular KernelsSIAM Journal on Mathematical Analysis, 1971