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A Fast Block Krylov Implicit Runge–Kutta Method for Solving Large-Scale Ordinary Differential Equations

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Optimization, Simulation, and Control

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 76))

Abstract

In this chapter, we describe a new based block Krylov–Runge–Kutta method for solving stiff ordinary differential equations. We transform the linear system arising in the application of Newton’s method to a nonsymmetric matrix Stein equation that will be solved by a block Krylov iterative method. Numerical examples are given to illustrate the performance of our proposed method.

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Authors and Affiliations

  1. LMPA, LMPA Universite du Littoral Cote d’Opale, 50 rue F. Buisson BP. 699, F-62228, Calais Cedex, France

    A. Bouhamidi & K. Jbilou

Authors
  1. A. Bouhamidi
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  2. K. Jbilou
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Corresponding author

Correspondence to K. Jbilou .

Editor information

Editors and Affiliations

  1. , Institute of Mathematics, National University of Mongolia, University Street 1, Ulaanbaatar, 210646, Erdenet, Mongolia

    Altannar Chinchuluun

  2. , Department of Industrial & Systems Engin, University of Florida, Weil Hall 401, Gainesville, 32611, Florida, USA

    Panos M. Pardalos

  3. The School of Economic Studies, Dept.of Mathematics & Computer Science, National University of Mongolia, Ulaanbaatar, 210646, Mongolia

    Rentsen Enkhbat

  4. , Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom

    E. N. Pistikopoulos

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Bouhamidi, A., Jbilou, K. (2013). A Fast Block Krylov Implicit Runge–Kutta Method for Solving Large-Scale Ordinary Differential Equations. In: Chinchuluun, A., Pardalos, P., Enkhbat, R., Pistikopoulos, E. (eds) Optimization, Simulation, and Control. Springer Optimization and Its Applications, vol 76. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5131-0_20

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