Phase-fitted Runge-Kutta pairs of orders 8(7)

A new phase fitted RungeKutta pair of orders 8(7) which is a modification of a well known explicit RungeKutta pair for the integration of periodic initial value problems is presented. Numerical experiments show the efficiency of the new pair in a wide range of oscillatory problems.

[1]  P. Brown.  A local convergence theory for combined inexact-Newton/finite-difference projection methods , 1987 .

[2]  Charalampos Tsitouras,et al.  Cheap Error Estimation for Runge-Kutta Methods , 1999, SIAM J. Sci. Comput..

[3]  E. Hairer,et al.  Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems , 1993 .

[4]  R. Van Dooren.  Stabilization of Cowell's classical finite difference method for numerical integration , 1974 .

[5]  George Papageorgiou,et al.  Runge-Kutta pairs for periodic initial value problems , 2005, Computing.

[6]  J. Butcher.  The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods , 1987 .

[7]  P. J. Van Der Houmen,et al.  Predictor-corrector methods for periodic second-order initial-value problems , 1987 .

[8]  S. N. Papakostas,et al.  High Phase-Lag-Order Runge-Kutta and Nyström Pairs , 1999, SIAM J. Sci. Comput..

[9]  J. Dormand,et al.  High order embedded Runge-Kutta formulae , 1981 .

[10]  E. Hairer,et al.  Solving Ordinary Differential Equations I , 1987 .

[11]  A. D. Raptis,et al.  A four-step phase-fitted method for the numerical integration of second order initial-value problems , 1991 .

[12]  W. Gautschi.  Numerical integration of ordinary differential equations based on trigonometric polynomials , 1961 .

[13]  Ben P. Sommeijer,et al.  Explicit Runge-Kutta (-Nyström) methods with reduced phase errors for computing oscillating solutions , 1987 .

[14]  E. Hairer,et al.  Solving Ordinary Differential Equations II , 2010 .

[15]  Theodore E. Simos,et al.  Explicit high order methods for the numerical integration of periodic initial-value problems , 1998, Appl. Math. Comput..

[16]  T. E. Simos,et al.  A P-Stable Eighth-Order Method for the Numerical Integration of Periodic Initial-Value Problems , 1997 .

[17]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .