Solutions of Emden–Fowler equations by homotopy-perturbation method

Chowdhury, Md. Sazzad Hossien; Hashim, Ishak

doi:10.1016/j.nonrwa.2007.08.017

Cited by 121 publications

(79 citation statements)

References 34 publications

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“…He [30] used HPM to solve the Lighthill equation, the Duffing equation [31], and the Blasius equation [32]. This method has also been used to solve nonlinear boundary value problems [33], integral equation [34][35][36], Klein-Gordon and Sine-Gordon equations [37], Emden-Flower-type equations [38], and several other problems [39][40][41]. Using homotopy perturbation method (refer to Appendix A), the approximate solution of (1) is…”

Section: For Small and Medium Values Of The Saturation Parameter α Anmentioning

confidence: 99%

Approximate Analytical Solution of Nonlinear Reaction’s Diffusion Equation at Conducting Polymer Ultramicroelectrodes

Anitha¹,

Alwarappan

Rajendran³

2012

ISRN Physical Chemistry

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A theoretical model of reaction/diffusion within conducting polymer microelectrodes is discussed. The model is based on the steady-state diffusion equation containing a nonlinear term related to the Michaelis-Menten kinetic of the enzymatic reaction. An analytical expression pertaining to the concentration of substrate and current is obtained using homotopy perturbation method for all values of diffusion and the saturation parameter. The substrate concentration profile and current response can be used in a large range of concentrations including the non-linear contributions. These approximate analytical results were found to be in good agreement with the previously reported limiting case results.

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Section: For Small and Medium Values Of The Saturation Parameter α Anmentioning

confidence: 99%

Approximate Analytical Solution of Nonlinear Reaction’s Diffusion Equation at Conducting Polymer Ultramicroelectrodes

Anitha¹,

Alwarappan

Rajendran³

2012

ISRN Physical Chemistry

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“…The physical structure of the solutions with a discussion of the formulation can be found in [2,3,5,10,14,17]. A general study has been given by Wazwaz [20,21] to construct both exact and series solutions to Emden-Fowler equations through Adomian decomposition method.…”

Section: Introductionmentioning

confidence: 99%

Bernstein polynomials method for numerical solutions of integro-differential form of the singular Emden-Fowler initial value problems

Bencheikh¹,

Chiter²,

Abbassi³

2017

J. Math. Computer Sci.

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In this paper, Bernstein polynomial method applied to the solutions of generalized Emden-Fowler equations as singular initial value problems is presented. Firstly, the singular differential equations are converted to Volterra integro-differential equations and then solved by the Bernstein polynomials method. The properties of Bernstein polynomials via Gauss-Legendre rule are used to reduce the integral equations to a system of algebraic equations which can be solved numerically. Some illustrative examples are discussed to demonstrate the validity and applicability of the present method.

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“…Approximate solutions to the Lane-Emden equation were given by implicit series solution [18] and the homotopy perturbation method [19,20]. In [21], the Boubaker polynomials expansion scheme is applied successfully in order to obtain analytical-numerical solutions for two kind of Lane-Emden problems.…”

Section: Introductionmentioning

confidence: 99%

Jacobi rational–Gauss collocation method for Lane–Emden equations of astrophysical significance

Doha

Bhrawy

Hafez

et al. 2014

NAMC

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Abstract. In this paper, a new spectral collocation method is applied to solve Lane-Emden equations on a semi-infinite domain. The method allows us to overcome difficulty in both the nonlinearity and the singularity inherent in such problems. This Jacobi rational-Gauss method, based on Jacobi rational functions and Gauss quadrature integration, is implemented for the nonlinear Lane-Emden equation. Once we have developed the method, numerical results are provided to demonstrate the method. Physically interesting examples include Lane-Emden equations of both first and second kind. In the examples given, by selecting relatively few Jacobi rational-Gauss collocation points, we are able to get very accurate approximations, and we are thus able to demonstrate the utility of our approach over other analytical or numerical methods. In this way, the numerical examples provided demonstrate the accuracy, efficiency, and versatility of the method.

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Solutions of Emden–Fowler equations by homotopy-perturbation method

Cited by 121 publications

References 34 publications

Approximate Analytical Solution of Nonlinear Reaction’s Diffusion Equation at Conducting Polymer Ultramicroelectrodes

Approximate Analytical Solution of Nonlinear Reaction’s Diffusion Equation at Conducting Polymer Ultramicroelectrodes

Bernstein polynomials method for numerical solutions of integro-differential form of the singular Emden-Fowler initial value problems

Jacobi rational–Gauss collocation method for Lane–Emden equations of astrophysical significance

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