Homotopy analysis method to obtain numerical solutions of the Painlevé equations

DOI10.1002/mma.2521zbMath1252.34020OpenAlexW2078905179MaRDI QIDQ2912308

H. Latifizadeh, Esmail Hesameddini

Publication date: 14 September 2012

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.2521

zbMATH Keywords

Painlevé equationshomotopy analysis method

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Related Items (3)

Numerical solution for complex systems of fractional order ⋮ A study on nonlinear wet fin problem using homotopy analysis method ⋮ Numerical study of the asymptotics of the second Painlevé equation by a functional fitting method

Cites Work

• Homotopy analysis of MHD boundary layer flow of an upper-convected Maxwell fluid
• Series solutions of non-linear Riccati differential equations with fractional order
• On exact solution of Laplace equation with Dirichlet and Neumann boundary conditions by the homotopy analysis method
• Application of homotopy analysis method to fractional KdV-Burgers-Kuramoto equation
• Applying homotopy analysis method for solving differential-difference equation
• Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method
• Homotopy analysis method for fractional IVPs
• Notes on the homotopy analysis method: some definitions and theorems
• A study of homotopy analysis method for limit cycle of van der Pol equation
• Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation
• Adaptation of homotopy analysis method for the numeric-analytic solution of Chen system
• The homotopy analysis method for multiple solutions of nonlinear boundary value problems
• The homotopy analysis method to solve the Burgers-Huxley equation
• Solitary wave solutions to the Kuramoto-Sivashinsky equation by means of the homotopy analysis method
• Rotating flow of a third-grade fluid in a porous space with Hall current
• Explicit series solution for the Glauert-jet problem by means of the homotopy analysis method
• Non-similar analytic solution for MHD flow and heat transfer in a third-order fluid over a stretching sheet
• The homotopy analysis method for handling systems of fractional differential equations
• A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations
• The essence of the homotopy analysis method
• The modified homotopy perturbation method for solving strongly nonlinear oscillators
• Series solution of nonlinear eigenvalue problems by means of the homotopy analysis method
• On the homotopy analysis method for nonlinear problems.
• Special polynomials associated with rational solutions of the fifth Painlevé equation
• Painlevé equations -- nonlinear special functions.
• An approximate solution technique not depending on small parameters: A special example
• The second Painlevé equation as a model for the electric field in a semiconductor.
• On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder
• Solitary smooth hump solutions of the Camassa-Holm equation by means of the homotopy analysis method
• The numerical solution of the second Painlevé equation
• An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method
• Beyond Perturbation

This page was built for publication: Homotopy analysis method to obtain numerical solutions of the Painlevé equations