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Two-step almost collocation methods for ordinary differential equations

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Abstract

A new class of two-step Runge-Kutta methods for the numerical solution of ordinary differential equations is proposed. These methods are obtained using the collocation approach by relaxing some of the collocation conditions to obtain methods with desirable stability properties. Local error estimation for these methods is also discussed.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Universitá di Salerno, Fisciano, Salerno, 84084, Italy

    R. D’Ambrosio & B. Paternoster

  2. Dipartimento di Matematica e Applicazioni, Universitá di Napoli - “Federico II”, 80126, Napoli, Italy

    M. Ferro

  3. Department of Mathematics and Statistics, Arizona State University, Tempe, AZ, 85287, USA

    Z. Jackiewicz

Authors
  1. R. D’Ambrosio
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  2. M. Ferro
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  3. Z. Jackiewicz
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  4. B. Paternoster
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Corresponding author

Correspondence to R. D’Ambrosio.

Additional information

The work of the third author was partially supported by the National Science Foundation under grant NSF DMS–0510813 and by Consiglio Nazionale delle Ricerche.

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D’Ambrosio, R., Ferro, M., Jackiewicz, Z. et al. Two-step almost collocation methods for ordinary differential equations. Numer Algor 53, 195–217 (2010). https://doi.org/10.1007/s11075-009-9280-5

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  • DOI: https://doi.org/10.1007/s11075-009-9280-5

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