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Approximate solution of a differential equation arising in astrophysics using the variational iteration method
Mehdi Dehghan,Fatemeh Shakeri +1 more
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In this article, a variational iteration method was used to solve the Lane-Emden equation for a self-gravitating, spherically symmetric polytropic fluid.About:
This article is published in New Astronomy.The article was published on 2008-01-01. It has received 206 citations till now. The article focuses on the topics: Lane–Emden equation & Partial differential equation.read more
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Solving nonlinear fractional partial differential equations using the homotopy analysis method
TL;DR: In this paper, the homotopy analysis method is applied to solve nonlinear fractional partial differential equations (FPDE) with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives, and the results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique.
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An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering
TL;DR: In this article, an elementary introduction to the concepts of the recently developed asymptotic methods and new developments is given, giving an intuitive grasp for Lagrange multiplier, calculus of variations, optimization, variational iteration method, parameterexpansion method, exp-function method, homotopy perturbation method, and ancient Chinese mathematics as well.
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An approximation algorithm for the solution of the nonlinear lane-emden type equations arising in astrophysics using hermite functions collocation method
TL;DR: A collocation method for solving some well-known classes of Lane–Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain based on a Hermite function collocation (HFC) method is proposed.
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Solutions of singular IVPs of Lane–Emden type by the variational iteration method
Ahmet Yildirim,Turgut Öziş +1 more
TL;DR: In this article, approximate-exact solutions of a class of Lane-Emden type singular IVPs problems, by the variational iteration method, are presented, which yields solutions in the forms of convergent series with easily calculable terms.
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Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type
TL;DR: A pseudospectral technique is proposed to solve the Lane-Emden type equations on a semi-infinite domain based on rational Legendre functions and Gauss-Radau integration to solve a system of nonlinear algebraic equations.
References
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Some asymptotic methods for strongly nonlinear equations
TL;DR: In this paper, a survey of recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones, is presented.
Book
The method of weighted residuals and variational principles
TL;DR: In this article, the method of Weighted Residuals is used to solve boundary-value problems in heat and mass transfer problems, and convergence and error bounds are established.
Journal ArticleDOI
Approximate analytical solution for seepage flow with fractional derivatives in porous media
TL;DR: In this article, a variational iteration method is used to give approximate solutions of the problem of seepage flow in porous media with fractional derivatives, and the results show that the proposed iteration method, requiring no linearization or small perturbation is very effective and convenient.