An efficient four‐step multiderivative method for the numerical solution of second‐order IVPs with oscillating solutions

Shokri, Ali; Khalsaraei, Mohammad Mehdizadeh

doi:10.1002/cmm4.1116

Cited by 2 publications

(1 citation statement)

References 33 publications

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“…In what follows, we will mention some references. The Runge–Kutta methods, 1–10 multistep methods, 11–17 and Runge–Kutta–Nyström methods 18–42 are some of the approaches that can be used for solving a second-order differential equation. Since the Störmer–Cowell multistep procedure with more than two steps suffers from orbital instability issues, some improved versions of the Störmer–Cowell method were proposed by Gautschi 8 and Stiefel and Bettis.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of second-order initial-value problems using a new class of variable coefficients and two-step semi-hybrid methods

et al. 2021

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In this paper, a new family of two-step semi-hybrid schemes of the 12th algebraic order is proposed for the numerical simulation of initial-value problems of second-order ordinary differential equations. The proposed methods are symmetric and belong to the family of multiderivative methods. Each method of the new family appears to be hybrid, but after implementing the hybrid terms, it will continue as a multiderivative method. Therefore, the designation semi-hybrid is used. The consistency, convergence, stability, and periodicity of the methods are investigated and analyzed. In order to show the accuracy, consistency, convergence, and stability of the proposed family, it was tested on some well-known problems, such as the undamped Duffing’s equation. The simulation results demonstrate the efficiency and advantages of the proposed method compared to the currently available methods.

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Section: Introductionmentioning

confidence: 99%

Numerical simulation of second-order initial-value problems using a new class of variable coefficients and two-step semi-hybrid methods

et al. 2021

Self Cite

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Variable order step size method for solving orbital problems with periodic solutions

Rasedee¹,

Jamaludin²,

Najib³

et al. 2022

Math. Model. Comput.

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Existing variable order step size numerical techniques for solving a system of higher-order ordinary differential equations (ODEs) requires direct calculating the integration coefficients at each step change. In this study, a variable order step size is presented for direct solving higher-order orbital equations. The proposed algorithm calculates the integration coefficients only once at the beginning and, if necessary, once at the end. The accuracy of the numerical approximation is validated with well-known orbital differential equations. To reduce computational costs, we obtain the relationship for the predictor-corrector algorithm between integration coefficients of various orders. The efficiency of the proposed method is substantiated by the graphical representation of accuracy at the total evaluation steps.

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An efficient four‐step multiderivative method for the numerical solution of second‐order IVPs with oscillating solutions

Cited by 2 publications

References 33 publications

Numerical simulation of second-order initial-value problems using a new class of variable coefficients and two-step semi-hybrid methods

Numerical simulation of second-order initial-value problems using a new class of variable coefficients and two-step semi-hybrid methods

Variable order step size method for solving orbital problems with periodic solutions

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