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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Stability results for one-step discretized collocation methods in the numerical treatment of Volterra integral equations


Authors: M. R. Crisci, E. Russo and A. Vecchio
Journal: Math. Comp. 58 (1992), 119-134
MSC: Primary 65R20; Secondary 45D05, 45L05
MathSciNet review: 1106963
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Abstract: This paper is concerned with the stability analysis of the discretized collocation method for the second-kind Volterra integral equation with degenerate kernel. A fixed-order recurrence relation with variable coefficients is derived, and local stability conditions are given independent of the discretization. Local stability and stability with respect to an isolated perturbation of some methods are proved. The reliability of the derived stability conditions is shown by numerical experiments.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1992-1106963-7
PII: S 0025-5718(1992)1106963-7
Keywords: Volterra integral equations, degenerate kernel, stability, discrete collocation methods, Runge-Kutta methods
Article copyright: © Copyright 1992 American Mathematical Society