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

Maria Jesus Moreta
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Maria Jesus Moreta: IMUVA. Departamento de Análisis Económico y Economía Cuantitativa, Campus de Somosaguas, Universidad Complutense de Madrid, Pozuelo de Alarcón, 28223 Madrid, Spain

Mathematics, 2021, vol. 9, issue 18, 1-20

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.

Keywords: second-order in time problems; non-linear problems; Rosenbrock type methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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