Peter Linz
Abstract
The Dahlquist stability analysis for ordinary differential equations is extended to the case of Volterra integro-differential equations. Thus the standard multistep methods can be generalized to furnish algorithms for solving integro-differential equations. Special starting procedures are discussed, and some numerical examples are presented.
- 1 DAHLQUIST, G. Convergence and stability in the numerical integration of ordinary differential equations. Math. Seand. 4 (1956), 33-53.Google Scholar
- 2 DAVIS, H. T. Introduction to Nonlinear Differential and Integral Equations. Dover, New York, 1962.Google Scholar
- 3 DAY, J .T . Note on the numerical solution of integro-differential equations. Comput. J. 9, 4 (Feb. 1967), 394-395.Google Scholar
- 4 HENRICI, P. Discrete Variable Methods in Ordinary Differential Equations. Wiley, New York, 1962.Google Scholar
- 5 POUZET, P. MEthode d'intEgration numdrique des dquations integrales et intdgro-differentielles du type de Volterra de seconde espece. Formules de Runge-Kutta, Symposium on the Numerical Treatment of Ordinary Differential Equations, Integral and Integrodifferential Equations, Rome, 1960, pp. 362-368.Google Scholar
Index Terms
- Linear Multistep Methods for Volterra Integro-Differential Equations
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