Approximate Solutions for the Nonlinear Third-Order Ordinary Differential Equations

Karahan, Mustafa

doi:10.1515/zna-2016-0502

Cited by 6 publications

(4 citation statements)

References 23 publications

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“…Mirzabeigy and Yildirim 10 obtained the periodic solution of the nonlinear third‐order equation utilizing the modified differential transform method. Jerk equations with cubic nonlinearities have gained their analytical solutions and period by the perturbation approach, the multiple scales method, and the Lindstedt–Poincaré method 14 . El‐Dib 15 obtained the criteria of vibration control in delayed third‐order critically damped Duffing oscillation by applying the modified homotopy perturbation method.…”

Section: Introductionmentioning

confidence: 99%

The simplest approach to solving the cubic nonlinear jerk oscillator with the non‐perturbative method

El‐Dib

2022

Math Methods in App Sciences

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Mathematics and its applications try to make available a simple and accurate approach to handle nonlinear equations. The present paper investigates for the first time the application of the linearizing method to determine both the approximate frequency and displacement amplitude for the third-order differential equations. The main merit of the linearized method is a collection of simplicity and accuracy for the solution of high-order nonlinear conservative or non-conservative oscillators. The current work sheds light on the approximate proposition to the damped third-order nonlinear differential equations.The fast estimated solution is simulated to the accurate solution gained through the numerical methods. It is significant to conclude that the nonperturbative method considered here is simpler and easier to apply than the other perturbation methods. This paper enriches some existing literature.

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Section: Introductionmentioning

confidence: 99%

The simplest approach to solving the cubic nonlinear jerk oscillator with the non‐perturbative method

El‐Dib

2022

Math Methods in App Sciences

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“…Moreover, a new technique based on classical HBM was implemented to find higher periodic approximations for the different types of non-linear differential equations, including various types of secondorder and more-than-second-order derivatives [9]. The multiple scales Lindstedt-Poincare (MSLP) approach was employed to identify approximate analytical solutions to jerk-type equations with cubic non-linearities [10]. Ramos [11] applied approximation techniques to analyze different types of non-linear jerk equations that have analytical periodic solutions.…”

Section: Introductionmentioning

confidence: 99%

On Perturbative Methods for Analyzing Third-Order Forced Van-der Pol Oscillators

et al. 2022

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In this investigation, an (un)forced third-order/jerk Van-der Pol oscillatory equation is solved using two perturbative methods called the Krylov–Bogoliúbov–Mitropólsky method and the multiple scales method. Both the first- and second-order approximations for the unforced and forced jerk Van-der Pol oscillatory equations are derived in detail using the proposed methods. Comparative analysis is performed between the analytical approximations using the proposed methods and the numerical approximations using the fourth-order Runge–Kutta scheme. Additionally, the global maximum error to the analytical approximations compared to the Runge–Kutta numerical approximation is estimated.

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“…ÇÖLP (Pakdemirli vd., 2009;Pakdemirli ve Karahan, 2010;Pakdemirli vd., 2011;Karahan ve Pakdemirli, 2017a;Karahan ve Pakdemirli, 2017b;Karahan, 2017)…”

Section: Introductionmentioning

confidence: 99%

Gergin Elastik Tele Bağlı Kütlenin Doğrusal Olmayan Salınımının Yaklaşık Çözümleri

Karahan¹,

Bostanci²

2019

Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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Öz Gergin elastik bir tele bağlı kütlenin doğrusal olmayan titreşim hareketi ele alınmıştır. Sistemin hareket denklemi oluşturulmuştur. Hareket denklemine çok ölçekli metot (ÇÖM) ve çok ölçekli Lindstedt Poincare (ÇÖLP) metodu uygulanmıştır. Belirtilen metotlar kullanılarak hareket denkleminin yaklaşık analitik çözümleri bulunmuştur. Belirtilen çözümler hareket denkleminin sayısal çözümü ile karşılaştırılmıştır. Kuvvetli doğrusal olmayan sistemlerde ÇÖLP metodu iyi sonuçlar vermiştir.

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Approximate Solutions for the Nonlinear Third-Order Ordinary Differential Equations

Cited by 6 publications

References 23 publications

The simplest approach to solving the cubic nonlinear jerk oscillator with the non‐perturbative method

The simplest approach to solving the cubic nonlinear jerk oscillator with the non‐perturbative method

On Perturbative Methods for Analyzing Third-Order Forced Van-der Pol Oscillators

Gergin Elastik Tele Bağlı Kütlenin Doğrusal Olmayan Salınımının Yaklaşık Çözümleri

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