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Rosenbrock Type Methods for Solving Non-Linear Second-Order in Time Problems

Author

Listed:
  • Maria Jesus Moreta

    (IMUVA. Departamento de Análisis Económico y Economía Cuantitativa, Campus de Somosaguas, Universidad Complutense de Madrid, Pozuelo de Alarcón, 28223 Madrid, Spain)

Abstract

In this work, we develop a new class of methods which have been created in order to numerically solve non-linear second-order in time problems in an efficient way. These methods are of the Rosenbrock type, and they can be seen as a generalization of these methods when they are applied to second-order in time problems which have been previously transformed into first-order in time problems. As they also follow the ideas of Runge–Kutta–Nyström methods when solving second-order in time problems, we have called them Rosenbrock–Nyström methods. When solving non-linear problems, Rosenbrock–Nyström methods present less computational cost than implicit Runge–Kutta–Nyström ones, as the non-linear systems which arise at every intermediate stage when Runge–Kutta–Nyström methods are used are replaced with sequences of linear ones.

Suggested Citation

  • Maria Jesus Moreta, 2021. "Rosenbrock Type Methods for Solving Non-Linear Second-Order in Time Problems," Mathematics, MDPI, vol. 9(18), pages 1-20, September.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2225-:d:633011
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