Application of Hybrid Functions for Solving Duffing-Harmonic Oscillator

Heydari, Mohammad; Loghmani, Ghasem Barid; Hosseini, Seyed Mohammad; Karbassi, S. M.

doi:10.1155/2014/210754

Cited by 7 publications

(5 citation statements)

References 36 publications

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“…A numerical method for finding the solution of Duffing-harmonic oscillator was proposed by [17]. The approach was based on hybrid functions approximation.…”

Section: Introductionmentioning

confidence: 99%

A proposed sixth order inverse polynomial method for the solution of non-linear physical models

Fadugba,

Ibrahim,

Adeyeye

et al. 2023

J. Math. Computer Sci.

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There are several nonlinear physical models emanated from science and technology that have always remained a challenge for numerical analysts and applied mathematicians. Various one-step numerical methods were developed to deal with these models, however, it requires the developed method to have consistency, stability, zero stability and convergence characteristics to handle the non-linearity in the model. This paper proposes a new sixth order inverse polynomial method (SOIPM) with a relative measure of stability for the solution of non-linear physical models with different flavors. Firstly, the properties of SOIPM are analyzed and investigated. Moreover, three illustrative non-linear physical models have been solved to measure the accuracy, computational performance, suitability and effectiveness of SOIPM. Furthermore, the results generated via SOIPM are compared with the existing method of the celebrated Runge-Kutta of order four (RK4) in the context of the exact value (EV). Finally, the absolute errors (ABEs) and final absolute errors (FABEs) incurred by SOIPM are computed and compared with that of RK4.

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“…A numerical method for finding the solution of Duffing-harmonic oscillator was proposed by [17]. The approach was based on hybrid functions approximation.…”

Section: Introductionmentioning

confidence: 99%

A proposed sixth order inverse polynomial method for the solution of non-linear physical models

Fadugba,

Ibrahim,

Adeyeye

et al. 2023

J. Math. Computer Sci.

View full text Add to dashboard Cite

show abstract

“…There are various numerical techniques based on different basis functions such as the Chebyshev polynomials (Nikooeinejad et al, 2016(Nikooeinejad et al, , 2017Nikooeinejad and Heydari, 2019;Avazzadeh and Heydari, 2012;Heydari et al, 2013a), radial basis function (Avazzadeh et al, 2011(Avazzadeh et al, , 2014Heydari et al, 2012a), Chebyshev cardinal functions (Avazzadeh and Heydari, 2017;Heydari et al, 2014Heydari et al, , 2013bHeydari et al, , 2012bLakestani and Dehghan, 2010) and Bernstein polynomials (Heydari et al, 2015(Heydari et al, , 2017Hosseini et al, 2017aHosseini et al, , 2017b to solve nonlinear differential equations. This research aims to follow an accurate and efficient direct method derived from the linear barycentric rational interpolation and its associated operational matrices of integral and product to approximate the three-dimensional nanofluid flow with heat and mass transfer caused by a horizontal nonlinearly stretching sheet in two lateral directions.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of three-dimensional nanofluid flow with heat and mass transfer on a nonlinearly stretching sheet using the barycentric functions

Torkaman

Loghmani

Heydari

et al. 2020

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Purpose The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel operational-matrix-based method. Design/methodology/approach The partial differential equations that governing the problem are converted into the system of nonlinear ordinary differential equations (ODEs) with considering suitable similarity transformations. A direct numerical method based on the operational matrices of integration and product for the linear barycentric rational basic functions is used to solve the nonlinear system of ODEs. Findings Graphical and tabular results are provided to illustrate the effect of various parameters involved in the problem on the velocity profiles, temperature distribution, nanoparticle volume fraction, Nusselt and Sherwood number and skin friction coefficient. Comparison between the obtained results, numerical results based on the Maple's dsolve (type = numeric) command and previous existing results affirms the efficiency and accuracy of the proposed method. Originality/value The motivation of the present study is to provide an effective computational method based on the operational matrices of the barycentric cardinal functions for solving the problem of three-dimensional nanofluid flow with heat and mass transfer. The convergence analysis of the presented scheme is discussed. The benefit of the proposed method (PM) is that, without using any collocation points, the governing equations are converted to the system of algebraic equations.

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“…We refer the readers to the articles in [7,9,20,23,27]. Applications with numerical solutions have been studied by several authors, see for example, [10,14,16,25].…”

Section: Introductionmentioning

confidence: 99%

Some new oscillation criteria for second-order hybrid differential equations

Chatzarakis¹,

Deepa

Nagajothi

et al. 2020

Hacettepe Journal of Mathematics and Statistics

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In this paper, we consider the second order hybrid differential equations. For this class of equations, we establish a new criterion to check whether all solutions of an equation, in this class, oscillate. We prove this criterion, using a generalized Riccati technique and an averaging method. The established oscillatory criteria have a distinct form, from all other relevant criteria, in the literature. We illustrate the validity of our results by means of various examples.

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Application of Hybrid Functions for Solving Duffing-Harmonic Oscillator

Cited by 7 publications

References 36 publications

A proposed sixth order inverse polynomial method for the solution of non-linear physical models

A proposed sixth order inverse polynomial method for the solution of non-linear physical models

Numerical investigation of three-dimensional nanofluid flow with heat and mass transfer on a nonlinearly stretching sheet using the barycentric functions

Some new oscillation criteria for second-order hybrid differential equations

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