Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay. (English) Zbl 0876.65089

Enright, W. H.; Hu, Min

Appl. Numer. Math. 24, No. 2-3, 175-190 (1997).

Explicit and implicit continuous Runge-Kutta methods (i.e., Runge-Kutta methods with dense output) are used for the numerical treatment of neutral Volterra integro-differential equations with delay. The order of convergence is investigated and it is shown that the arising nonlinear systems can be solved by fixed point iteration as long as the considered problem is non-stiff. A few numerical experiments are included.

Reviewer: E.Hairer (Genève)

MSC:

65R20	Numerical methods for integral equations
45J05	Integro-ordinary differential equations

Keywords:

Runge-Kutta methods; dense output; neutral Volterra integro-differential equations; delay equations; convergence; fixed point iteration; numerical experiments

Software:

RODAS

References:

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