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Numerical treatments for Volterra delay integro-differential equations. (English) Zbl 1184.65122
Summary: This paper presents a new technique for numerical treatments of Volterra delay integro-differential equations that have many applications in biological and physical sciences. The technique is based on the mono-implicit Runge-Kutta method for treating the differential part and the collocation method (using Boole’s quadrature rule) for treating the integral part. The efficiency and stability properties of this technique are studied. Numerical results are presented to demonstrate the effectiveness of the methodology.

MSC:
65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
45J05 Integro-ordinary differential equations
Software:
dde23
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