Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the Second Kind
- 1 October 1985
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 45 (172) , 463-469
- https://doi.org/10.2307/2008136
Abstract
Fractional powers of linear multistep methods are suggested for the numerical solution of weakly singular Volterra integral equations. The proposed methods are convergent of the order of the underlying multistep method, also in the generic case of solutions which are not smooth at the origin. The stability properties (stability region, A-stability, $A(\alpha )$-stability) are closely related to those of the underlying linear multistep method.Keywords
This publication has 13 references indexed in Scilit:
- Discretized Fractional CalculusSIAM Journal on Mathematical Analysis, 1986
- A Stability Analysis of Convolution Quadraturea for Abel-Volterra Integral EquationsIMA Journal of Numerical Analysis, 1986
- Fast Numerical Solution of Nonlinear Volterra Convolution EquationsSIAM Journal on Scientific and Statistical Computing, 1985
- Product integration methods for second-kind Abel integral equationsJournal of Computational and Applied Mathematics, 1984
- The numerical solution of integral equations with weakly singular kernelsPublished by Springer Nature ,1984
- On the Stability of Linear Multistep Methods for Volterra Convolution EquationsIMA Journal of Numerical Analysis, 1983
- Runge-Kutta Theory for Volterra and Abel Integral Equations of the Second KindMathematics of Computation, 1983
- A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equationsJournal of Computational and Applied Mathematics, 1982
- Numerial Methods for Volterra Integral Equations with Singular KernelsSIAM Journal on Numerical Analysis, 1969
- A special stability problem for linear multistep methodsBIT Numerical Mathematics, 1963