On the General Solution to the Bratu and Generalized Bratu Equations

Koudahoun, L. H.; Akande, J.; Adjaï, D. K. K.; Kpomahou, Y. J. F.; Monsia, M. D.

doi:10.3844/jmssp.2018.193.200

Cited by 4 publications

(2 citation statements)

References 9 publications

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“…Instead one must rely on numerical tools and approximations such as Taylor, Adomian (2; 11), variational iteration (4; 9), asymptotic expansion (3), perturbation-iteration (1), Morgan-Voyce approach (7), homotopy perturbation (14) or Lie symmetry method. Another popular method is based on Sundman linearization approach (10). Polyanin's literature (12) has three possible analytical solutions that are condition dependent.…”

Section: Introductionmentioning

confidence: 99%

Exact Solution to Bratu Second Order Differential Equation.

Szewczyk¹

2023

Preprint

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The aim of this paper is to analytically derive the exact solution to general type of Bratu second order differential equation. The method used to obtain this solution is based on substitution and algebra. Furthermore, new additional formulas are derived for existing solutions of Bratu equation found in Polyanin's literature. The results are compared with numerical solutions using Maxima, a computer algebra system program capable of numerical and symbolic computation. In this present study, summary of existing and new solutions with general boundary conditions allows researcher and students select a convenient formula that may provide a valuable information about relationship between terms, variables and coefficients which can be very useful for theoretical physics.

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Section: Introductionmentioning

confidence: 99%

Exact Solution to Bratu Second Order Differential Equation.

Szewczyk¹

2023

Preprint

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“…It was also used to model the dynamic behavior of a cargo system [24]. It is interesting to point out that this model without damping has been obtained in the modeling of the purely elastic structures whose the tension was related to the normal strain by a power law [25]. The equation 2is an extended form of cubic damped Duffing oscillator defined by (1).…”

Section: Introductionmentioning

confidence: 99%

Chaotic Dynamics of an Extended Duffing Oscillator Under Periodic Excitation

Koudahoun¹

2018

WJAP

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In this paper, chaotic dynamics of a cubic-quintic-septic Duffing oscillator subjected to periodic excitation is investigated. The multiple scales method is used to determine the various resonance states of the model. It is found that the considered model posses thirteen resonance states whose seven are thoroughly studied. The steady-state solutions and theirs stabilities are determined. The frequency-amplitude curves show that the considered system presents mixed behavior, limit cycles, hysteresis, jump and bifurcation phenomena. It is also noticed that these phenomena are strongly influenced by quintic-septic nonlinearity and excitation amplitude. Bifurcation structures displayed by the model for each considered type of resonant states are investigated numerically using the fourth-order Runge-Kutta algorithm. As results, the quintic-septic nonlinearity, linear dissipation and excitation amplitude can be used to control the chaotic behavior of the system.

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