Non-dissipative extended one-step methods for oscillatory problems

We examine stability of the class of extended one-step methods introduced in Chawla et al. [6] for the numerical integration of first-order initial-value problems y′ = f(t,y)y (t 0 ) = η, which possess oscillating solutions. We first characterize those methods which are non-dissipative for the integ...

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Bibliographic Details
Published in:International journal of computer mathematics 1998-01, Vol.69 (1-2), p.85-100
Main Authors: Chawla, M. M., Al-Zanaidi, M. A.
Format: Article
Language:English
Subjects:
Exact sciences and technology
extended one-step methods
G.1.7
Initial-value problem
Lorenz system
Mathematics
non-dissipative methods
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
ordinary differential equations
oscillating solutions
predator-prey oscillations
Sciences and techniques of general use
Simpson's rule
Van der Pol oscillator
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Summary:We examine stability of the class of extended one-step methods introduced in Chawla et al. [6] for the numerical integration of first-order initial-value problems y′ = f(t,y)y (t 0 ) = η, which possess oscillating solutions. We first characterize those methods which are non-dissipative for the integration of problems with oscillating solutions, and then derive non-dissipative methods of orders two to five. Interestingly, a modified version of Simpson's rule is shown to be non-dissipative for the integration of oscillatory problems. The obtained methods are numerically tested on problems taken from real-world applications.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207169808804711