On the numerical solutions of some Volterra equations on infinite intervals

Olavi Nevanlinna

Authors

Olavi Nevanlinna Helsinki University of Technology, Institute of Mathematics, Netherlands

Keywords:

Volterrra equations, positive quadratures, \(A\)-stable multistep methods, monotone mappings. MSC, 65R99, 65L04, 65L20.

Abstract views: 489

Abstract

The paper discusses long time behavior and error bounds for discretized Volterra equations. A key property is positivity of the quadrature which is combined with monotonicity properties of the nonlinearities in the equations. It is shown how the positivity of discretization quadrature is linked with \(A\)-stability property of linear multistep methods for ordinary differential equations. Some of the results are new when applied to differential equations with monotone nonlinearities and \(A\)-stable discretizations.

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References

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