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

In: Optimization, Simulation, and Control

Author

Listed:
  • A. Bouhamidi

    (LMPA Universite du Littoral Cote d’Opale)

  • K. Jbilou

    (LMPA Universite du Littoral Cote d’Opale)

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.

Suggested Citation

  • A. Bouhamidi & K. Jbilou, 2013. "A Fast Block Krylov Implicit Runge–Kutta Method for Solving Large-Scale Ordinary Differential Equations," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & E. N. Pistikopoulos (ed.), Optimization, Simulation, and Control, edition 127, pages 319-330, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-5131-0_20
    DOI: 10.1007/978-1-4614-5131-0_20
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    Cited by:

    1. Sarker, Pratik & Chakravarty, Uttam K, 2020. "A generalization of the method of lines for the numerical solution of coupled, forced vibration of beams," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 115-142.

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