scholarly journals A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems

1984 ◽  
Vol 11 (3) ◽  
pp. 277-281 ◽  
Author(s):  
M.M. Chawla ◽  
P.S. Rao
Keyword(s):  
Initial Value Problems ◽  
Second Order ◽  
Phase Lag ◽  
Initial Value ◽  
Type Method ◽  
Periodic Initial Value Problems ◽  
Minimal Phase

AN EXPLICIT HIGH ORDER PREDICTOR-CORRECTOR METHOD FOR PERIODIC INITIAL VALUE PROBLEMS

1995 ◽  
Vol 05 (02) ◽  
pp. 159-166 ◽  
Author(s):  
T.E. SIMOS
Keyword(s):  
Initial Value Problems ◽  
Interval Of Periodicity ◽  
Phase Lag ◽  
Initial Value ◽  
Large Interval ◽  
Type Method ◽  
Algebraic Order ◽  
Periodic Initial Value Problems ◽  
Orbit Equation ◽  
Predictor Corrector

An explicit Runge-Kutta type method is developed here. This method has an algebraic order six, a large interval of periodicity and a phase-lag of order eight. It is much more efficient than other well known methods when applying to an orbit equation.

A FAMILY OF HYBRID EIGHTH ORDER METHODS WITH MINIMAL PHASE-LAG FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION AND RELATED PROBLEMS

2000 ◽  
Vol 11 (02) ◽  
pp. 415-437 ◽  
Author(s):  
G. AVDELAS ◽  
A. KONGUETSOF ◽  
T. E. SIMOS
Keyword(s):  
Numerical Solution ◽  
Initial Value Problems ◽  
Hybrid Methods ◽  
Phase Lag ◽  
Initial Value ◽  
Eighth Order ◽  
New Methods ◽  
Algebraic Order ◽  
Periodic Initial Value Problems ◽  
Minimal Phase

In this paper a family of hybrid methods with minimal phase-lag are developed for the numerical solution of periodic initial-value problems. The methods are of eighth algebraic order and have large intervals of periodicity. The efficiency of the new methods is presented by their application to the wave equation and to coupled differential equations of the Schrödinger type.

ON THE CONSTRUCTION OF EFFICIENT METHODS FOR SECOND ORDER IVPS WITH OSCILLATING SOLUTION

2001 ◽  
Vol 12 (10) ◽  
pp. 1453-1476 ◽  
Author(s):  
T. E. SIMOS ◽  
JESUS VIGO AGUIAR
Keyword(s):  
Initial Value Problems ◽  
Multistep Methods ◽  
Oscillating Solution ◽  
Second Order ◽  
Phase Lag ◽  
Initial Value ◽  
New Methods ◽  
Oscillating Solutions ◽  
Exponentially Fitted ◽  
Minimal Phase

In this paper we describe procedures for the construction of efficient methods for the numerical solution of second order initial value problems (IVPs) with oscillating solutions. Based on the described procedures we develop two simple and efficient multistep methods for the solution of the above problems. The first method is exponentially-fitted and trigonometrically-fitted and the second has a minimal phase-lag. Both methods are symmetric. Numerical results obtained for several well known problems show the efficiency of the new methods when they are compared with known methods in the literature.

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