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Runge–Kutta–collocation methods for systems of functional–differential and functional equations

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Abstract

Systems of functional–differential and functional equations occur in many biological, control and physics problems. They also include functional–differential equations of neutral type as special cases. Based on the continuous extension of the Runge–Kutta method for delay differential equations and the collocation method for functional equations, numerical methods for solving the initial value problems of systems of functional–differential and functional equations are formulated. Comprehensive analysis of the order of approximation and the numerical stability are presented.

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  1. Gonville and Caius College, Cambridge University, Cambridge, CB2 1TA, UK

    Yunkang Liu

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  1. Yunkang Liu
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Liu, Y. Runge–Kutta–collocation methods for systems of functional–differential and functional equations. Advances in Computational Mathematics 11, 315–329 (1999). https://doi.org/10.1023/A:1018936328525

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