Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method

DOI10.1016/j.physleta.2007.05.094zbMath1209.65104OpenAlexW2139354281MaRDI QIDQ716007

A. Sami Bataineh, Ishak Hashim, Mohd. Salmi Md. Noorani

Publication date: 19 April 2011

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2007.05.094

zbMATH Keywords

homotopy analysis methodtime-dependent Lane-Emden equationwave-type equationtime-dependent emden-fowler equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items (55)

Falkner-Skan flow of a Maxwell fluid with heat transfer and magnetic field ⋮ A modified homotopy perturbation method for singular time dependent Emden-Fowler equations with boundary conditions ⋮ Mixed convection flow of a micropolar fluid with radiation and chemical reaction ⋮ Buckling of Euler columns with a continuous elastic restraint via homotopy analysis method ⋮ Control of error in the homotopy analysis of solutions to the Zakharov system with dissipation ⋮ Homotopy analysis method to obtain numerical solutions of the Painlevé equations ⋮ On series solution for generalized Falkner-Skan flow of a FENE-P model ⋮ Solving partial fractional differential equations by using the Laguerre wavelet-Adomian method ⋮ Heat transfer and flows of thermal convection in a fluid-saturated rotating porous medium ⋮ Falkner-Skan wedge flow of a power-law fluid with mixed convection and porous medium ⋮ Haar wavelet collocation method for solving singular and nonlinear fractional time-dependent Emden-Fowler equations with initial and boundary conditions ⋮ Optimal homotopy analysis and control of error for solutions to the non-local Whitham equation ⋮ A new analytical technique to solve Fredholm's integral equations ⋮ Series solutions of nano boundary layer flows by means of the homotopy analysis method ⋮ Melting heat transfer in a boundary layer flow of a second grade fluid under Soret and Dufour effects ⋮ Mathematical properties of \(\hbar\)-curve in the frame work of the homotopy analysis method ⋮ Approximate solutions of singular two-point BVPs by modified homotopy analysis method ⋮ Analytic solution for MHD Falkner-Skan flow over a porous surface ⋮ A new technique of using homotopy analysis method for second order nonlinear differential equations ⋮ The approximate solutions of Fredholm integrodifferential-difference equations with variable coefficients via homotopy analysis method ⋮ The homotopy analysis method and the Liénard equation ⋮ An efficient analytic approach for solving two-point nonlinear boundary value problems by homotopy analysis method ⋮ Local fractional homotopy analysis method for solving non-differentiable problems on Cantor sets ⋮ Approximate analytical solutions of systems of PDEs by homotopy analysis method ⋮ Solution method for the transformed time-dependent Michaelis-Menten enzymatic reaction model ⋮ Method for constructing analytical solutions to the Dym initial value problem ⋮ A new analytical technique to solve Volterra's integral equations ⋮ Series solution of the multispecies Lotka-Volterra equations by means of the homotopy analysis method ⋮ On the choice of auxiliary linear operator in the optimal homotopy analysis of the Cahn-Hilliard initial value problem ⋮ Predictor homotopy analysis method: two points second order boundary value problems ⋮ Control of error in the homotopy analysis of semi-linear elliptic boundary value problems ⋮ Unique and multiple PHAM series solutions of a class of nonlinear reactive transport model ⋮ Some notes on using the homotopy perturbation method for solving time-dependent differential equations ⋮ Comparison of three semi-analytical methods for solving \((1+1)\)-dimensional dispersive long wave equations ⋮ The homotopy analysis method for Cauchy reaction-diffusion problems ⋮ A study on the convergence of homotopy analysis method ⋮ On convergence of homotopy analysis method and its modification for fractional modified KdV equations ⋮ An efficient analytical approach for solving fourth order boundary value problems ⋮ Notes on the homotopy analysis method: some definitions and theorems ⋮ Homotopy analysis method for singular IVPs of Emden-Fowler type ⋮ Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation ⋮ A new application of the homotopy analysis method: solving the Sturm-Liouville problems ⋮ Predictor homotopy analysis method and its application to some nonlinear problems ⋮ On a new reliable modification of homotopy analysis method ⋮ Modified homotopy analysis method for solving systems of second-order BVPs ⋮ Prediction of multiplicity of solutions of nonlinear boundary value problems: novel application of homotopy analysis method ⋮ Multilayer perceptron and Chebyshev polynomials based neural network for solving Emden-Fowler type initial value problems ⋮ Homotopy analysis method for multiple solutions of the fractional Sturm-Liouville problems ⋮ Analytical solution for time-dependent flow of a third grade fluid induced due to impulsive motion of a flat porous plate ⋮ Efficient low-error analytical-numerical approximations for radial solutions of nonlinear Laplace equations ⋮ Numerical treatment of nonlinear Emden-Fowler equation using stochastic technique ⋮ Solving nonlinear differential equations in astrophysics and fluid mechanics using the generalized pseudospectral method ⋮ Direct solution of \(n\)th-order IVPs by homotopy analysis method ⋮ An adaptation of homotopy analysis method for reliable treatment of strongly nonlinear problems: construction of homotopy polynomials ⋮ Exact and analytical solutions for a nonlinear sigma model

Cites Work

• Exact flow of a third grade fluid past a porous plate using homotopy analysis method
• Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid
• An explicit, totally analytic approximate solution for Blasius' viscous flow problems
• The application of homotopy analysis method to nonlinear equations arising in heat transfer
• A new branch of solutions of boundary-layer flows over an impermeable stretched plate
• Numerically solving nonlinear problems by the homotopy analysis method
• Homotopy analysis method: A new analytic method for nonlinear problems.
• Solution of physical problems by decomposition
• A kind of approximation solution technique which does not depend upon small parameters. II: An application in fluid mechanics
• On the homotopy analysis method for nonlinear problems.
• Explicit analytic solution for similarity boundary layer equations.
• Adomian decomposition method for a reliable treatment of the Emden-Fowler equation
• A new method for solving singular initial value problems in the second-order ordinary differential equations
• An approximate solution technique not depending on small parameters: A special example
• Homotopy perturbation technique
• Analytical solution for the time-dependent Emden--Fowler type of equations by Adomian decomposition method
• The modified decomposition method for analytic treatment of differential equations
• Homotopy solutions for a generalized second-grade fluid past a porous plate
• Comparison between the homotopy analysis method and homotopy perturbation method
• Nonperturbative approximate solution for Lane–Emden equation
• Beyond Perturbation
• Application of variational iteration method to a general Riccati equation
• SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS
• A new algorithm for solving differential equations of Lane-Emden type
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method