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Two Step Runge-Kutta-Nyström Methods For Oscillatory Problems Based On Mixed Polynomials

B. Paternoster
Published 2003 · Mathematics, Computer Science

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We consider two step Runge-Kutta-Nystrom methods for the numerical integration of y″ = f(x, y) having periodic or oscillatory solutions. We assume that the frequency ω can be estimated in advance. Using the linear stage representation, we describe how to derive two step Runge-Kutta-Nystrom methods which integrate trigonometric and mixed polynomials exactly. The resulting methods depend on the parameter v = ωh, where h is the stepsize.
This paper references
Exponentially fitted Runge-Kutta methods
G. V. Berghe (2000)
Numerical integration of ordinary differential equations based on trigonometric polynomials
W. Gautschi (1961)
A new theoretical approach to RK methods
P. Albrecht (1987)
Elements of a general theory of composite integration methods
P. Albrecht (1989)
Two Step Runge-Kutta-Nyström Methods for y'' = f(x, y) and P-Stability
B. Paternoster (2002)
A new theoretical approach to RK methods, SIAM J
P. Albrecht (1987)
Operations on oscillatory functions
L. Ixaru (1997)
Runge–Kutta(–Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials, Appl
B. Paternoster (1998)
Two-step Runge-Kutta methods
Z. Jackiewicz (1991)
A note on the capacitance matrix algorithm, substructuring, and mixed or Neumann boundary conditions
B. Paternoster (1987)
An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions
T. Simos (1998)
Mixed collocation methods for y ′′ =f x,y
J. P. Coleman (2000)
P-stability and exponential-fitting methods for y″″ = f(x, y)
J. P. Coleman (1996)
A phase–fitted collocation–based Runge–Kutta–Nyström method, Appl
B. Paternoster (2000)
A new theoretical approach to Runge-Kutta methods
P. Albrecht (1987)
General two–step Runge–Kutta methods based on algebraic and trigonometric polynomials, Int
B. Paternoster (2001)
General two – step Runge – Kutta methods based on algebraic and trigonometric polynomials
B. Paternoster (2001)
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
J. Butcher (1987)
Frequency determination and step-length control for exponentially-fitted Runge---Kutta methods
G. V. Berghe (2001)
Runge-Kutta(-Nystro¨m) methods for ODEs with periodic solutions based on trigonometric polynomials
B. Paternoster (1998)
A phase – fitted collocation – based Runge – Kutta – Nyström method
B. Paternoster (2000)
A conditionally P-stable fourth-order exponential-fitting method for y '' = f ( f, y )
L. Ixaru (1999)
Operations on oscillatory functions, Comput
Ixaru (1997)

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