Abstract
A four-step method with phase-lag of infinite order is developed for the numerical integration of second order initial-value problems. Extensive numerical testing indicates that this new method can be generally more accurate than other four-step methods.
Similar content being viewed by others
References
M. M. Chawla and P. S. Rao,A Numerov-type method with minimal phase-lag for the numerical integration of second order periodic initial-value problem, J. Comput. Appl. Math. 11 (1984), 277–281.
M. M. Chawla and P. S. Rao,A Numerov-type method with minimal phase-lag for the integration of second order periodic initial-value problem. II. Explicit method, J. Comput. Appl. Math. 15 (1986), 329–337.
M. M. Chawla, P. S. Rao and B. Neta,Two-step fourth-order P-stable methods with phase-lag of order six for y″=f(t,y), J. Comput. Appl. Math. 16 (1986), 233–236.
M. M. Chawla and P. S. Rao,An explicit sixth-order method with phase-lag or order eight for y″=f(t,y), J. Comput. Appl. Math. 17 (1987), 365–368.
R. M. Thomas,Phase properties of high order, almost P-stable formulae, BIT 24 (1984), 225–238.
P. J. Van der Houwen and B. P. Sommeijer,Predictor-corrector methods for periodic second-order initial-value problems, IMA J. Num. Anal. 7 (1987), 407–422.
J. P. Coleman,Numerical methods for y″=f(x,y) via rational approximations for the cosine, IMA J. Num. Anal. 9 (1989), 145–165.
E. Stiefel and D. G. Bettis,Stabilization of Cowell's method, Num. Math. 13 (1969), 154–175.
P. Henrici,Discrete Variable Methods in Ordinary Differential Equations, (1962), 311, John Wiley and Sons.
R. K. Jain, N. S. Kambo and R. Goel,A sixth-order P-stable symmetric multistep method for periodic initial-value problems of second-order differential equations, IMA J. Num. Anal. 4 (1984), 117–125.
A. D. Raptis,Two-step methods for the numerical solution of the Schrödinger equation, Computing 28 (1982), 373–378.
R. A. Buckingham,Numerical Solution of Ordinary and Partial Differential Equations, (1962), Pergamon Press.
J. W. Cooley,An improved eigenvalue corrector formula for solving the Schrödinger equation for central fields, Math. Comput. 15 (1961), 363–374.
L. Brusa and L. Nigro,A one-step method for direct integration of structural dynamic equations, Internat. J. Numer. Meth. Engng. 15 (1980), 685–699.
W. Liniger and R. A. Willoughby,Efficient integration methods for stiff systems of ordinary differential equations, SIAM J. Num. Anal. 7 (1970), 47–66.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Raptis, A.D., Simos, T.E. A four-step phase-fitted method for the numerical integration of second order initial-value problems. BIT 31, 160–168 (1991). https://doi.org/10.1007/BF01952791
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01952791