Rosenbrock Type Methods for Solving Non-Linear Second-Order in Time Problems
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-orde...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-09-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/18/2225 |
| _version_ | 1797518356347092992 |
|---|---|
| author | Maria Jesus Moreta |
| author_facet | Maria Jesus Moreta |
| author_sort | Maria Jesus Moreta |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T07:27:46Z |
| format | Article |
| id | doaj.art-28090623f32b4ec3b43406b1afb5b1e1 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T07:27:46Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-28090623f32b4ec3b43406b1afb5b1e12023-11-22T14:05:11ZengMDPI AGMathematics2227-73902021-09-01918222510.3390/math9182225Rosenbrock Type Methods for Solving Non-Linear Second-Order in Time ProblemsMaria Jesus Moreta0IMUVA. Departamento de Análisis Económico y Economía Cuantitativa, Campus de Somosaguas, Universidad Complutense de Madrid, Pozuelo de Alarcón, 28223 Madrid, SpainIn 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.https://www.mdpi.com/2227-7390/9/18/2225second-order in time problemsnon-linear problemsRosenbrock type methods |
| spellingShingle | Maria Jesus Moreta Rosenbrock Type Methods for Solving Non-Linear Second-Order in Time Problems Mathematics second-order in time problems non-linear problems Rosenbrock type methods |
| title | Rosenbrock Type Methods for Solving Non-Linear Second-Order in Time Problems |
| title_full | Rosenbrock Type Methods for Solving Non-Linear Second-Order in Time Problems |
| title_fullStr | Rosenbrock Type Methods for Solving Non-Linear Second-Order in Time Problems |
| title_full_unstemmed | Rosenbrock Type Methods for Solving Non-Linear Second-Order in Time Problems |
| title_short | Rosenbrock Type Methods for Solving Non-Linear Second-Order in Time Problems |
| title_sort | rosenbrock type methods for solving non linear second order in time problems |
| topic | second-order in time problems non-linear problems Rosenbrock type methods |
| url | https://www.mdpi.com/2227-7390/9/18/2225 |
| work_keys_str_mv | AT mariajesusmoreta rosenbrocktypemethodsforsolvingnonlinearsecondorderintimeproblems |