Embedded implicit Runge–Kutta Nyström method for solving second-order differential equations
IR@C-MMACS: CSIR-Centre for Mathematical Modelling and Computer Simulation, Bangalore
View Archive Info| Field | Value | |
| Title |
Embedded implicit Runge–Kutta Nyström method
for solving second-order differential equations
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| Creator |
T R, Ramamohan
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| Subject |
Mathematical Modelling & Simulations
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| Description |
An embedded diagonally implicit Runge–Kutta Nyström (RKN) method is constructed for the
integration of initial-value problems for second-order ordinary differential equations possessing oscillatory
solutions. This embedded method is derived using a three-stage diagonally implicit RKN
method of order four within which a third-order three stage diagonally implicit RKN method is
embedded. We demonstrate how this system can be solved, and by an appropriate choice of free
parameters, we obtain an optimized RKN(4,3) embedded algorithm. We also examine the intervals
of stability and show that the method is strongly stable within an appropriate region of
stability and is thus suitable for oscillatory problems by applying the method to the test equation
y
__ = −ω2y, ω > 0. Necessary and sufficient conditions are given for this method to possess nonvanishing
intervals of periodicity, for the fourth-order method. Finally, we present the coefficients of
the method optimized for small truncation errors. This new scheme is likely to be efficient for the
numerical integration of second-order differential equations with periodic solutions, using adaptive
step size.
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| Publisher |
Taylor & Francis
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| Date |
2006-11-08
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| Type |
Article
PeerReviewed |
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| Format |
application/pdf
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| Identifier |
http://cir.cmmacs.ernet.in/95/1/imoni.pdf
T R, Ramamohan (2006) Embedded implicit Runge–Kutta Nyström method for solving second-order differential equations. International Journal of Computer Mathematics, 83 (11). pp. 777-784. ISSN 0020-7160 |
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| Relation |
http://www.tandf.co.uk/journals
http://cir.cmmacs.ernet.in/95/ |
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