A new phase-fitted eight-step symmetric embedded predictor–corrector method (EPCM) for orbital problems and related IVPs with oscillating solutions

Panopoulos, G. A.; Simos, T. E.

doi:10.1016/j.cpc.2013.10.005

Cited by 25 publications

(3 citation statements)

References 24 publications

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“…• the embedded multistep method which was produced using the eighth algebraic order explicit eight-step method developed by Quinlan and Tremaine [4] and the embedded predictor-corrector tenth algebraic order eight-step method developed by Panapoulos and Simos [34] which is indicated as Method V…”

Section: Coupled Differential Equationsmentioning

confidence: 99%

High algebraic order Runge–Kutta type two-step method with vanished phase-lag and its first, second, third, fourth, fifth and sixth derivatives

Ning

Simos

2015

Computer Physics Communications

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Section: Coupled Differential Equationsmentioning

confidence: 99%

High algebraic order Runge–Kutta type two-step method with vanished phase-lag and its first, second, third, fourth, fifth and sixth derivatives

Ning

Simos

2015

Computer Physics Communications

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“…(i) Methods with constant coefficients (see [9,7,[10][11][12][13]) and (ii) Methods with coefficients dependent on the frequency of the problem (phase-fitted methods, exponentially-fitted methods and trigonometrically-fitted methods for second-order ODEs) (see [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]). …”

Section: Introductionmentioning

confidence: 99%

An eight-step semi-embedded predictor–corrector method for orbital problems and related IVPs with oscillatory solutions for which the frequency is unknown

Panopoulos

Simos

2015

Journal of Computational and Applied Mathematics

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109

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a b s t r a c tOur new linear symmetric semi-embedded predictor-corrector method (SEPCM) presented here is based on the multistep symmetric method of Quinlan and Tremaine (1990), with eight steps and eighth algebraic order and constructed to solve numerically the twodimensional Kepler problem. It can also be used to integrate related IVPs with oscillatory solutions for which the frequency is unknown. Firstly we present a SEPCM (see Panopoulos and Simos, 2013 [36,37]) in pair form. This form has the advantage that reduces the computational expense. From this form we construct a new symmetric eight-step method. The new scheme has constant coefficients and algebraic order ten. We tested the efficiency of our newly developed scheme against some well known methods from the literature. We measure the efficiency of the methods and conclude that the new scheme is the most efficient of all the compared methods and for all the problems solved.

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“…We call the above method Embedded Predictor-Corrector Method (EPCM), in the sense that the predictor method is fully contained in the corrector method (see [8]). …”

Section: The M-step Embedded Predictor-corrector (Epcm) Pair Formmentioning

confidence: 99%

A New Optimized Symmetric Embedded Predictor- Corrector Method (EPCM) for Initial-Value Problems with Oscillatory Solutions

Panopoulos¹,

Simos²,

Arabia³

2014

Appl. Math. Inf. Sci.

122

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Abstract:In this work a new optimized symmetric eight-step embedded predictor-corrector method (EPCM) with minimal phase-lag and algebraic order ten is presented. The method is based on the symmetric multistep method of Quinlan-Tremaine [1], with eight steps and eighth algebraic order and is constructed to solve numerically IVPs with oscillatory solutions. We compare the new method to some recently constructed optimized methods and other methods from the literature. We measure the efficiency of the methods and conclude that the new optimized method with minimal phase-lag is noticeably most efficient of all the compared methods and for all the problems solved including the two-dimensional Kepler problem and the radial Schrödinger equation.

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A new phase-fitted eight-step symmetric embedded predictor–corrector method (EPCM) for orbital problems and related IVPs with oscillating solutions

Cited by 25 publications

References 24 publications

High algebraic order Runge–Kutta type two-step method with vanished phase-lag and its first, second, third, fourth, fifth and sixth derivatives

High algebraic order Runge–Kutta type two-step method with vanished phase-lag and its first, second, third, fourth, fifth and sixth derivatives

An eight-step semi-embedded predictor–corrector method for orbital problems and related IVPs with oscillatory solutions for which the frequency is unknown

A New Optimized Symmetric Embedded Predictor- Corrector Method (EPCM) for Initial-Value Problems with Oscillatory Solutions

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