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.
| Language | English |
|---|---|
| Pages | 589-606 |
| Number of pages | 18 |
| Journal | Applied Mathematics and Computation |
| Volume | 247 |
| DOIs | |
| Publication status | Published - 15 Nov 2014 |
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Keywords
- Differential equation
- Dynamical systems
- Local Linearization
- Numerical integrator
- Runge-Kutta
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Locally Linearized Runge Kutta method of Dormand and Prince. / Jimenez, J. C.; Sotolongo, A.; Sanchez-Bornot, J. M.
In: Applied Mathematics and Computation, Vol. 247, 15.11.2014, p. 589-606.Research output: Contribution to journal › Article
TY - JOUR
T1 - Locally Linearized Runge Kutta method of Dormand and Prince
AU - Jimenez, J. C.
AU - Sotolongo, A.
AU - Sanchez-Bornot, J. M.
PY - 2014/11/15
Y1 - 2014/11/15
N2 - 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.
AB - 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.
KW - Differential equation
KW - Dynamical systems
KW - Local Linearization
KW - Numerical integrator
KW - Runge-Kutta
UR - http://www.scopus.com/inward/record.url?scp=84907736354&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2014.09.001
DO - 10.1016/j.amc.2014.09.001
M3 - Article
VL - 247
SP - 589
EP - 606
JO - Applied Mathematics and Computation
T2 - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
ER -