Locally Linearized Runge Kutta method of Dormand and Prince

J. C. Jimenez, A. Sotolongo, J. M. Sanchez-Bornot

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

LanguageEnglish
Pages589-606
Number of pages18
JournalApplied Mathematics and Computation
Volume247
DOIs
Publication statusPublished - 15 Nov 2014

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Runge Kutta methods
Runge-Kutta Methods
Runge-Kutta
Initial value problems
Linearization
Initial Value Problem
Computational Cost
Computer simulation
High Accuracy
Imply
Costs
Numerical Simulation
Simulation

Keywords

  • Differential equation
  • Dynamical systems
  • Local Linearization
  • Numerical integrator
  • Runge-Kutta

Cite this

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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 journalArticle

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