On comparison of series and numerical solutions for second Painlevé equation

DOI10.1002/num.20475zbMath1197.65080OpenAlexW2027467829WikidataQ115398464 ScholiaQ115398464MaRDI QIDQ5747611

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Publication date: 14 September 2010

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.20475

zbMATH Keywords

convergencecomparison of methodsnumerical examplesseries solutionsecond Painlevé equationAdomian decomposition methodhomotopy analysis methodhomotopy perturbation methodLegendre tau methodanalytic continuation method

Mathematics Subject Classification ID

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) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (5)

Homotopy Analysis Method and Time-fractional NLSE with Double Cosine, Morse, and New Hyperbolic Potential Traps ⋮ The use of a Legendre pseudospectral viscosity technique to solve a class of nonlinear dynamic Hamilton-Jacobi equations ⋮ Comparison of three semi-analytical methods for solving \((1+1)\)-dimensional dispersive long wave equations ⋮ An efficient numerical treatment for the asymptotic behaviour of the nonlinear Airy-type problems ⋮ Series solution for heat transfer from a continuous surface in a parallel free stream of viscoelastic fluid

Cites Work

• Analytical solutions for pipe flow of a fourth grade fluid with Reynold and Vogel's models of viscosities
• Thin film flow of an unsteady shrinking sheet through porous medium with variable viscosity
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• Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt
• The application of homotopy analysis method to nonlinear equations arising in heat transfer
• The application of homotopy analysis method to thin film flows of a third order fluid
• A new branch of solutions of boundary-layer flows over an impermeable stretched plate
• Comparison of HAM and HPM methods in nonlinear heat conduction and convection equations
• The influence of slip condition on thin film flow of a fourth grade fluid by the homotopy analysis method
• An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate
• Comparison between the homotopy analysis method and homotopy perturbation method
• Beyond Perturbation

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