P-Stable Obrechkoff Methods with Minimal Phase-Lag for Periodic Initial Value Problems

1987 ◽  
Vol 49 (180) ◽  
pp. 553 ◽  
Author(s):  
U. Ananthakrishnaiah
Keyword(s):  
Initial Value Problems ◽  
Phase Lag ◽  
Initial Value ◽  
Obrechkoff Methods ◽  
Periodic Initial Value Problems ◽  
Minimal Phase

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.

A P-stable complete in phase Obrechkoff trigonometric fitted method for periodic initial-value problems

1993 ◽  
Vol 441 (1912) ◽  
pp. 283-289 ◽  
Keyword(s):  
Initial Value Problems ◽  
Numerical Results ◽  
New Method ◽  
Phase Lag ◽  
Initial Value ◽  
Periodic Initial Value Problems

In this paper we derive a P-stable trigonometric fitted Obrechkoff method with phase-lag (frequency distortion) infinity. It is easy to see, from numerical results presented, that the new method is much more accurate than previous methods.

An improved trigonometrically fitted P-stable Obrechkoff method for periodic initial-value problems

2005 ◽  
Vol 461 (2058) ◽  
pp. 1639-1658 ◽  
Author(s):  
Zhongcheng Wang ◽  
Deying Zhao ◽  
Yongming Dai ◽  
Dongmei Wu
Keyword(s):  
Initial Value Problems ◽  
New Method ◽  
Order Derivative ◽  
Phase Lag ◽  
Initial Value ◽  
Numerical Illustration ◽  
First Order ◽  
Derivative Formula ◽  
Periodic Initial Value Problems

In this paper we present an improved P-stable trigonometrically fitted Obrechkoff method with phase-lag (frequency distortion) infinity. Compared with the previous P-stable trigonometrically fitted Obrechkoff method developed by Simos, our new method is simpler in structure and more stable in computation. We have also improved the accuracy of the first-order derivative formula. From the numerical illustration presented, we can show that the new method is much more accurate than the previous methods.

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.

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