Generalization of the Störmer method for perturbed oscillators without explicit first derivatives

In this work we construct a numerical method specially designed for perturbed oscillators without explicit first derivatives. The new method, which generalizes the classical Störmer and Cowell codes for second-order equations, is useful when the calculation of the first derivative is not needed beca...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 111; no. 1; pp. 123 - 132
Main Authors López, David J., Martı́n, Pablo, Farto, José M.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Amsterdam Elsevier B.V 15.11.1999
Elsevier
Subjects
Exact sciences and technology
Mathematics
Multistep method
Numerical analysis
Numerical analysis. Scientific computation
Numerical integration
Ordinary differential equations
Perturbed oscillator
Sciences and techniques of general use
Multistep method
Perturbed oscillator
Numerical integration
Second order equation
Generating function
Cowell code
Differential equation
Initial value problem
Bettis method
Taylor series
Runge Kutta method
Störmer method
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Summary:In this work we construct a numerical method specially designed for perturbed oscillators without explicit first derivatives. The new method, which generalizes the classical Störmer and Cowell codes for second-order equations, is useful when the calculation of the first derivative is not needed because this derivative is not computed. Some numerical examples of the artificial satellite problem show the good behaviour of the methods when they compete against classical multistep and Runge–Kutta–Nyström codes.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(99)00136-3