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.

A PHASE-FITTED AND AMPLIFICATION-FITTED EXPLICIT TWO-STEP HYBRID METHOD FOR SECOND-ORDER PERIODIC INITIAL VALUE PROBLEMS

2006 ◽  
Vol 17 (05) ◽  
pp. 663-675 ◽  
Author(s):  
HANS VAN DE VYVER
Keyword(s):  
Hybrid Method ◽  
Initial Value Problems ◽  
Numerical Results ◽  
New Method ◽  
Test Problems ◽  
Phase Lag ◽  
Initial Value ◽  
Periodic Initial Value Problems ◽  
Free Parameters ◽  
Fifth Order

In this paper a phase-fitted and amplification-fitted explicit two-step hybrid method is introduced. The construction is based on a modification of a fifth-order dissipative method recently developed by Franco.19 Two free parameters are added in order to nullify the phase-lag and the amplification. Numerical results obtained for well-known test problems show the efficiency of the new method when it is compared with other existing codes.

A P-STABLE EIGHTEENTH-ORDER SIX-STEP METHOD FOR PERIODIC INITIAL VALUE PROBLEMS

2007 ◽  
Vol 18 (03) ◽  
pp. 419-431 ◽  
Author(s):  
CHUNFENG WANG ◽  
ZHONGCHENG WANG
Keyword(s):  
Initial Value Problems ◽  
Numerical Results ◽  
New Method ◽  
Initial Value ◽  
Step Method ◽  
Periodic Initial Value Problems

In this paper we present a new kind of P-stable eighteenth-order six-step method for periodic initial-value problems. We add the fourth derivatives to our previous P-stable six-step method to increase the accuracy. We apply two classes of well-known problems to our new method and compare it with the previous methods. The numerical results show that the new method is much more stable, accurate and efficient than the 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.

A HIGHLY ACCURATE AND EFFICIENT TRIGONOMETRICALLY-FITTED P-STABLE THREE-STEP METHOD FOR PERIODIC INITIAL-VALUE PROBLEMS

2006 ◽  
Vol 17 (04) ◽  
pp. 545-560
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI ◽  
DONGMEI WU
Keyword(s):  
Initial Value Problems ◽  
The Other ◽  
New Method ◽  
Phase Lag ◽  
Initial Value ◽  
Step Method ◽  
Eighth Order ◽  
Numerical Illustration ◽  
Even Order ◽  
Periodic Initial Value Problems

In this paper we present a new three-step method, which is a trigonometrically-fitted P-stable Obrechkoff method with phase-lag (frequency distortion) infinity. In this new method, we make use of higher-even-order derivatives including the eighth-order to increase the accuracy. On the other hand, we adopt a special structure to reduce the computational complexity of high-derivatives. The numerical illustration demonstrate that the new method has advantage in accuracy, periodic stability and efficiency.

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.

NUMEROV-TYPE METHODS FOR OSCILLATORY LINEAR INITIAL VALUE PROBLEMS

2009 ◽  
Vol 20 (03) ◽  
pp. 383-398 ◽  
Author(s):  
I. TH. FAMELIS
Keyword(s):  
Initial Value Problems ◽  
New Method ◽  
Phase Lag ◽  
Initial Value ◽  
Oscillatory Solutions ◽  
Type Method ◽  
Numerical Tests ◽  
Oscillating Solutions ◽  
Algebraic Order ◽  
High Phase

We present a new explicit Numerov-type method for the solution of second-order linear initial value problems with oscillating solutions. The new method attains algebraic order seven at a cost of six function evaluations per step. The method has the characteristic of zero dissipation and high phase-lag order making it suitable for the solution of problems with oscillatory solutions. The numerical tests in a variety of problems justify our effort.

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