Abstract
In this paper, the effect that produces the Local Linearization of the embedded Runge-Kutta formulas of Dormand and Prince for initial value problems is studied. For this, embedded Locally Linearized Runge-Kutta formulas are defined and their performance is analyzed by means of exhaustive numerical simulations. For a variety of well-known test equations with different dynamics, the simulation results show that the locally linearized formulas exhibit significant higher accuracy than the original ones, which implies a substantial reduction of the number of time steps and, consequently, a sensitive reduction of the overall computational cost of their adaptive implementation.
| Original language | English |
|---|---|
| Pages (from-to) | 589-606 |
| Number of pages | 18 |
| Journal | Applied Mathematics and Computation |
| Volume | 247 |
| DOIs | |
| Publication status | Published - 15 Nov 2014 |
Keywords
- Differential equation
- Dynamical systems
- Local Linearization
- Numerical integrator
- Runge-Kutta
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Jimenez, J. C., Sotolongo, A., & Sanchez-Bornot, J. M. (2014). Locally Linearized Runge Kutta method of Dormand and Prince. Applied Mathematics and Computation, 247, 589-606. https://doi.org/10.1016/j.amc.2014.09.001