A Functionally-Fitted Block Numerov Method for Solving Second-Order Initial-Value Problems with Oscillatory Solutions

Abdulganiy, R. I.; Ramos, Higinio; Akinfenwa, O. A.; Okunuga, S. A.

doi:10.1007/s00009-021-01879-2

Cited by 5 publications

(2 citation statements)

References 42 publications

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“…Furthermore, Figures 4, 5 and 6 respectively depict the trajectories in the phase plane flow using proposed BHA, BHA developed by [2] and the exact flow N = 160. For more details on Kepler equations, see [29][30][31][32][33][34][35].…”

Section: Numerical Examplesmentioning

confidence: 99%

An Accuracy-preserving Block Hybrid Algorithm for the Integration of Second-order Physical Systems with Oscillatory Solutions

Sunday

Ndam

Kwari

2023

J. Nig. Soc. Phys. Sci.

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It is a known fact that in most cases, to integrate an oscillatory problem, higher order A-stable methods are often needed. This is because such problems are characterized by stiffness, chaos and damping, thus making them tedious to solve. However, in this research, an accuracy-preserving relatively lower order Block Hybrid Algorithm (BHA) is proposed for solution of second-order physical systems with oscillatory solutions. The sixth order algorithm was derived using interpolation and collocation of power series within a single step interval [tn; tn+1]. In order to circumvent the Dahlquist-barrier and also obtain an accuracy-preserving algorithm, four o-step points were incorporated within the single step interval. A number of special cases of oscillatory problems were solved using the proposed method and the results obtained clearly showed that it outperformed other existing methods we compared our results with even though the BHA is of lower order relative to such methods. Some of the second-order physical systems considered were the Kepler, Bessel and damped problems. Some important properties of the BHA were also analyzed and the results of the analysis showed that it is consistent, zero-stable and convergent

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Section: Numerical Examplesmentioning

confidence: 99%

An Accuracy-preserving Block Hybrid Algorithm for the Integration of Second-order Physical Systems with Oscillatory Solutions

Sunday

Ndam

Kwari

2023

J. Nig. Soc. Phys. Sci.

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show abstract

“…A lot of numerical techniques have been derived for approximating stiff differential equations ranging from trigonometrically fitted methods, nonstandard finite difference methods, and others. See the works of [5][6][7][8][9][10][11][12][13]. All these methods are constant step methods where the step length is fixed.…”

Section: Definition 2 ([4]mentioning

confidence: 99%

Variable Step Hybrid Block Method for the Approximation of Kepler Problem

2022

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In this article, a variable step size strategy is adopted in formulating a new variable step hybrid block method (VSHBM) for the solution of the Kepler problem, which is known to be a rigid and stiff differential equation. To derive the VSHBM, the step size ratio r is left the same, halved, or doubled in order to optimize the total number of steps, minimize the number of formulae stored in the code, and ensure that the method is zero-stable. The method is formulated by integrating the Lagrange polynomial with limits of integration selected at special points. The article further analyzed the stability, order, consistency, and convergence properties of the VSHBM. The stability regions of the VSHBM at different values of the step size ratios were also plotted and plots showed that the method is fit for solving the Kepler problem. The results generated were then compared with some existing methods, including the MATLAB inbuilt stiff solver (ode 15 s), with respect to total number of failure steps, total number of steps, total function calls, maximum error, and computation time.

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A functionally-fitted block hybrid Falkner method for Kepler equations and related problems

Abdulganiy,

Ramos,

Osilagun

et al. 2023

Comp. Appl. Math.

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A Functionally-Fitted Block Numerov Method for Solving Second-Order Initial-Value Problems with Oscillatory Solutions

Cited by 5 publications

References 42 publications

An Accuracy-preserving Block Hybrid Algorithm for the Integration of Second-order Physical Systems with Oscillatory Solutions

An Accuracy-preserving Block Hybrid Algorithm for the Integration of Second-order Physical Systems with Oscillatory Solutions

Variable Step Hybrid Block Method for the Approximation of Kepler Problem

A functionally-fitted block hybrid Falkner method for Kepler equations and related problems

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