Optimal homotopy analysis method for nonlinear differential equations in the boundary layer

DOI10.1007/s11075-012-9587-5zbMath1260.65096OpenAlexW2060509999MaRDI QIDQ1935395

Tao Fan, Xiang-Cheng You

Publication date: 15 February 2013

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-012-9587-5

zbMATH Keywords

global optimizationconvergencenumerical examplesnonlinear differential equationscomputational efficiencyseries solutionsoptimal homotopy analysis methodsimilarity and non-similarity boundary layer equations

Mathematics Subject Classification ID

Boundary value problems for nonlinear higher-order PDEs (35G30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Series solutions to PDEs (35C10) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items (13)

Numerical and analytical solutions for Falkner-Skan flow of MHD Maxwell fluid ⋮ The optimal homotopy analysis method applied on nonlinear time‐fractional hyperbolic partial differential equation<scp>s</scp> ⋮ Heat transfer analysis of Williamson fluid over exponentially stretching surface ⋮ Mixed convective Williamson nanofluid flow over a rotating disk with zero mass flux ⋮ AN OPTIMAL HOMOTOPY ANALYSIS METHOD BASED ON PARTICLE SWARM OPTIMIZATION: APPLICATION TO FRACTIONAL-ORDER DIFFERENTIAL EQUATION ⋮ Impact of Linear Operator on the Convergence of HAM Solution: a Modified Operator Approach ⋮ Mixed convective flow of a Casson fluid over a vertical stretching sheet ⋮ MHD flow and heat transfer over a slender elastic permeable sheet in a rotating fluid with Hall current ⋮ Laplace transform for the solution of higher order deformation equations arising in the homotopy analysis method ⋮ Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind ⋮ Series solutions of non-similarity boundary layer flows of nano-fluids over stretching surfaces ⋮ An open problem on the optimality of an asymptotic solution to Duffing's nonlinear oscillation problem ⋮ A HAM-based analytic approach for physical models with an infinite number of singularities

Cites Work

• Notes on the homotopy analysis method: some definitions and theorems
• An optimal homotopy-analysis approach for strongly nonlinear differential equations
• A one-step optimal homotopy analysis method for nonlinear differential equations
• An explicit, totally analytic approximate solution for Blasius' viscous flow problems
• An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate
• Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls
• An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method
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