A New Symmetric p-stable Obrechkoff Method with Optimal Phase lag for Oscillatory Problems

In this paper, we derive a class of symmetric p-stable Obrechkoff methods via Padé approximation approach (PAA) for the numerical solution of special second order initial value problems (IVPs) in ordinary differential equations (ODEs). We investigate periodicity analysis on the proposed scheme to verify p-stability property. The new algorithms possess minimum phase-lag error which shows that they can accurately solve oscillatory problems. Reports on several numerical experiments are provided to illustrate the accuracy of the method.

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

Mathematics of Computation ◽

10.2307/2008328 ◽

1987 ◽

Vol 49 (180) ◽

pp. 553 ◽

Cited By ~ 38

Author(s):

U. Ananthakrishnaiah

Keyword(s):

Initial Value Problems ◽

Phase Lag ◽

Initial Value ◽

Obrechkoff Methods ◽

Periodic Initial Value Problems ◽

Minimal Phase

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$P$-stable Obrechkoff methods with minimal phase-lag for periodic initial value problems

Mathematics of Computation ◽

10.1090/s0025-5718-1987-0906188-x ◽

1987 ◽

Vol 49 (180) ◽

pp. 553-553 ◽

Cited By ~ 2

Author(s):

U. Anantha Krishnaiah

Keyword(s):

Initial Value Problems ◽

Phase Lag ◽

Initial Value ◽

Obrechkoff Methods ◽

Periodic Initial Value Problems ◽

Minimal Phase

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High phase-lag order trigonometrically fitted two-step Obrechkoff methods for the numerical solution of periodic initial value problems

Numerical Algorithms ◽

10.1007/s11075-014-9847-7 ◽

2014 ◽

Vol 68 (2) ◽

pp. 337-354 ◽

Cited By ~ 8

Author(s):

Ali Shokri ◽

Hosein Saadat

Keyword(s):

Numerical Solution ◽

Initial Value Problems ◽

Phase Lag ◽

Initial Value ◽

Obrechkoff Methods ◽

Periodic Initial Value Problems ◽

High Phase

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Symmetric multistep Obrechkoff methods with zero phase-lag for periodic initial value problems of second order differential equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2011.07.040 ◽

2011 ◽

Cited By ~ 2

Author(s):

Sujatha D. Achar

Keyword(s):

Differential Equations ◽

Initial Value Problems ◽

Second Order ◽

Phase Lag ◽

Initial Value ◽

Second Order Differential Equations ◽

Obrechkoff Methods ◽

Periodic Initial Value Problems ◽

Zero Phase

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A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

Numerical Mathematics Theory Methods and Applications ◽

10.4208/nmtma.2016.m1429 ◽

2016 ◽

Vol 9 (4) ◽

pp. 619-639 ◽

Cited By ~ 3

Author(s):

Zhong-Qing Wang ◽

Jun Mu

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Collocation Method ◽

Initial Value Problems ◽

Numerical Experiments ◽

High Order Accuracy ◽

Nonlinear Ordinary Differential Equations ◽

Initial Value ◽

Order Accuracy ◽

Long Time

AbstractWe introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain thehp-version bound on the numerical error of the multiple interval collocation method underH1-norm. Numerical experiments confirm the theoretical expectations.

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A family of two-step almostP-stable methods with phase-lag of order infinity for the numerical integration of second order periodic initial-value problems

Japan Journal of Industrial and Applied Mathematics ◽

10.1007/bf03167577 ◽

1993 ◽

Vol 10 (2) ◽

pp. 289-297 ◽

Cited By ~ 5

Author(s):

T. E. Simos

Keyword(s):

Numerical Integration ◽

Initial Value Problems ◽

Second Order ◽

Phase Lag ◽

Initial Value ◽

Periodic Initial Value Problems

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A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: explicit method

Journal of Computational and Applied Mathematics ◽

10.1016/0377-0427(86)90224-4 ◽

1986 ◽

Vol 15 (3) ◽

pp. 329-337 ◽

Cited By ~ 215

Author(s):

M.M. Chawla ◽

P.S. Rao

Keyword(s):

Initial Value Problems ◽

Second Order ◽

Phase Lag ◽

Explicit Method ◽

Initial Value ◽

Type Method ◽

Periodic Initial Value Problems ◽

Minimal Phase

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Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPS

Sains Malaysiana ◽

10.17576/jsm-2021-5006-25 ◽

2021 ◽

Vol 50 (6) ◽

pp. 1799-1814

Author(s):

Norazak Senu ◽

Nur Amirah Ahmad ◽

Zarina Bibi Ibrahim ◽

Mohamed Othman

Keyword(s):

Fourth Order ◽

Initial Value Problems ◽

Numerical Experiments ◽

Numerical Study ◽

Kutta Method ◽

Initial Value ◽

First Order ◽

Runge Kutta Method ◽

Runge Kutta ◽

The Stability

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

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EXPLICIT EIGHTH ORDER NUMEROV-TYPE METHODS WITH REDUCED NUMBER OF STAGES FOR OSCILLATORY IVPs

International Journal of Modern Physics C ◽

10.1142/s0129183108012625 ◽

2008 ◽

Vol 19 (06) ◽

pp. 957-970 ◽

Cited By ~ 9

Author(s):

I. Th. FAMELIS

Keyword(s):

Initial Value Problems ◽

Computational Cost ◽

Phase Lag ◽

Initial Value ◽

Eighth Order ◽

Oscillatory Solutions ◽

Numerical Tests ◽

New Methods ◽

Oscillating Solutions ◽

Algebraic Order

Using a new methodology for deriving hybrid Numerov-type schemes, we present new explicit methods for the solution of second order initial value problems with oscillating solutions. The new methods attain algebraic order eight at a cost of eight function evaluations per step which is the most economical in computational cost that can be found in the literature. The methods have high amplification and phase-lag order characteristics in order to suit to the solution of problems with oscillatory solutions. The numerical tests in a variety of problems justify our effort.

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

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1993.0061 ◽

1993 ◽

Vol 441 (1912) ◽

pp. 283-289 ◽

Cited By ~ 32

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.

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