On the homotopy analysis method for nonlinear problems.

DOI10.1016/S0096-3003(02)00790-7zbMath1086.35005OpenAlexW2144522870MaRDI QIDQ1412621

Shi-Jun Liao

Publication date: 25 November 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(02)00790-7

zbMATH Keywords

NonlinearHomotopy analysis methodAnalyticSimilar boundary-layerStretching wall

Mathematics Subject Classification ID

Boundary-layer theory, separation and reattachment, higher-order effects (76D10) Other special methods applied to PDEs (35A25)

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a semi-infinite flat plate ⋮ Numerical solution of nonlinear Volterra-Fredholm integro-differential equations using homotopy analysis method ⋮ Explicit series solution of travelling waves with a front of Fisher equation ⋮ Solving solitary waves with discontinuity by means of the homotopy analysis method ⋮ Wavelet basis expansion-based Volterra kernel function identification through multilevel excitations ⋮ Homotopy solutions for a generalized second-grade fluid past a porous plate ⋮ Numerical treatment for the solution of fractional fifth-order Sawada-Kotera equation using second kind Chebyshev wavelet method ⋮ A new approximate analytical method for ODEs ⋮ Homotopy simulation of nanofluid dynamics from a non-linearly stretching isothermal permeable sheet with transpiration ⋮ A frequency criterion for doubly clamped beam-type N/MEMS subjected to the van der Waals attraction ⋮ Solution of the one-phase inverse Stefan problem by using the homotopy analysis method ⋮ Mathematical analysis of an enzyme-entrapped conducting polymer modified electrode ⋮ Analytical solution for time-dependent flow of a third grade fluid induced due to impulsive motion of a flat porous plate ⋮ Homotopy analysis method for the sine-Gordon equation with initial conditions ⋮ New analytical method for gas dynamics equation arising in shock fronts ⋮ Explicit dispersion relation for strongly nonlinear flexural waves using the homotopy analysis method ⋮ Fractional generalised homotopy analysis method for solving nonlinear fractional differential equations ⋮ Comparative study of a cubic autocatalytic reaction via different analysis methods ⋮ Modified approach to solve nonlinear equation arising in infiltration phenomenon ⋮ Approximate analytical solution of two coupled time fractional nonlinear Schrödinger equations ⋮ q-homotopy analysis method for solving the seventh-order time-fractional Lax's Korteweg-de Vries and Sawada-Kotera equations ⋮ On the explicit, purely analytic solution of von Kármán swirling viscous flow ⋮ An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate ⋮ An analytic approach to solve multiple solutions of a strongly nonlinear problem ⋮ Comparison between the homotopy analysis method and homotopy perturbation method ⋮ Solving the Klein-Gordon equation by means of the homotopy analysis method ⋮ A new iterative technique for a fractional model of nonlinear Zakharov-Kuznetsov equations via Sumudu transform ⋮ An efficient numerical algorithm for the fractional Drinfeld-Sokolov-Wilson equation ⋮ A spectral method for the electrohydrodynamic flow in a circular cylindrical conduit ⋮ On the application of the homotopy analysis method for a nonlocal mixed problem with Bessel operator ⋮ Coupled flow and heat transfer in viscoelastic fluid with Cattaneo-Christov heat flux model ⋮ An efficient perturbation Sumudu transform technique for the time-fractional vibration equation with a memory dependent fractional derivative in Liouville-Caputo sense ⋮ An efficient numerical approach for fractional multidimensional diffusion equations with exponential memory ⋮ Describing function method with pointwise balancing in time domain for periodic responses of non-smooth self-excited system ⋮ A STUDY OF THE HEPATITIS B VIRUS INFECTION USING HILFER FRACTIONAL DERIVATIVE ⋮ Nonlinear control for soliton interactions in optical fiber systems ⋮ Accessing the thermodynamics of Walter‐B fluid with magnetic dipole effect past a curved stretching surface ⋮ On model for flow of Burgers nanofluid with Cattaneo-Christov double diffusion ⋮ On three-dimensional flow of couple stress fluid with Cattaneo-Christov heat flux ⋮ A revised model for Darcy-Forchheimer flow of Maxwell nanofluid subject to convective boundary condition ⋮ On exact solutions for time-fractional Korteweg-de Vries and Korteweg-de Vries-Burger's equations using homotopy analysis transform method ⋮ Dynamics of magnetohydrodynamic nonlinear radiative flow of diamond‐Co₃O₄/EG hybrid nanofluid with homogeneous—heterogeneous reactions ⋮ Three-dimensional flow of nanofluid with heat and mass flux boundary conditions ⋮ Radiative flow of Powell-Eyring Nanofluid with convective boundary conditions ⋮ Assessment of irreversibility optimization in Casson nanofluid flow with leading edge accretion or ablation ⋮ Simulating the joint impact of temporal and spatial memory indices via a novel analytical scheme ⋮ Fractional sight analysis of generalized perturbed Zakharov-Kuznetsov equation using Elzaki transform ⋮ A study on the flow of couple stress fluid in a porous curved channel ⋮ Applications of New Iterative Method to fractional non linear coupled ITO system ⋮ Three-dimensional flow of Jeffrey fluid with Cattaneo-Christov heat flux: an application to non-Fourier heat flux theory ⋮ Multivalued behavior for a two-level system using homotopy analysis method ⋮ An iterative method for time-fractional Swift-Hohenberg equation ⋮ A new analytical modelling for fractional telegraph equation via Laplace transform ⋮ Analytical solution for the time fractional BBM-Burger equation by using modified residual power series method ⋮ Singularly perturbed homotopy analysis method ⋮ Flow of micropolar fluid between parallel plates with Soret and Dufour effects ⋮ A new numerical algorithm for fractional Fitzhugh-Nagumo equation arising in transmission of nerve impulses ⋮ Time-dependent three-dimensional boundary layer flow of a Maxwell fluid ⋮ Convergent power series of \(\operatorname{sech}(x)\) and solutions to nonlinear differential equations ⋮ A numerical solution of fractional Lienard's equation by using the residual power series method ⋮ A modified analytical approach for fractional discrete KdV equations arising in particle vibrations ⋮ Numeric-analytic solutions of mixed-type systems of balance laws ⋮ A simple modification of homotopy perturbation method for the solution of Blasius equation in semi-infinite domains ⋮ Heat and mass transfer for MHD viscoelastic fluid flow over a vertical stretching sheet with considering soret and dufour effects ⋮ Utilizing feed-back neural network approach for solving linear Fredholm integral equations system ⋮ Analytical expressions for the concentrations of substrate, oxygen and mediator in an amperometric enzyme electrode ⋮ A homotopy series solution to a nonlinear partial differential equation arising from a mathematical model of the counter-current imbibition phenomenon in a heterogeneous porous medium ⋮ On the generalized wavelet-Galerkin method ⋮ MHD flow and heat transfer over a porous shrinking surface with velocity slip and temperature jump ⋮ Series solutions of non-Newtonian nanofluids with Reynolds model and Vogel's model by means of the homotopy analysis method ⋮ A Maple package of automated derivation of homotopy analysis solution for periodic nonlinear oscillations ⋮ Homotopy analysis method to Walter's B fluid in a vertical channel with porous wall ⋮ MHD stagnation flow of a micropolar fluid through a porous medium ⋮ On spectral homotopy analysis method for solving linear Volterra and Fredholm integrodifferential equations ⋮ Numerical solution for fractional model of Fokker-Planck equation by using q-HATM ⋮ Optimal homotopy asymptotic method for convective-radiative cooling of a lumped system, and convective straight fin with temperature-dependent thermal conductivity ⋮ The homotopy analysis method applied to the Kolmogorov-Petrovskii-Piskunov (KPP) and fractional KPP equations ⋮ A new approach for solving a class of nonlinear integro-differential equations ⋮ Analytic approximate solutions for MHD boundary-layer viscoelastic fluid flow over continuously moving stretching surface by homotopy analysis method with two auxiliary parameters ⋮ Analytical study for time and time-space fractional Burgers' equation ⋮ An efficient computational approach for generalized Hirota-Satsuma coupled KdV equations arising in shallow water waves ⋮ Heat and mass transfer in three-dimensional flow of an Oldroyd-B nanofluid with gyrotactic micro-organisms ⋮ Analytical investigation of laminar viscoelastic fluid flow over a wedge in the presence of buoyancy force effects ⋮ On the optimal selection of the linear operator and the initial approximation in the application of the homotopy analysis method to nonlinear fractional differential equations ⋮ New iterative technique for solving a system of nonlinear equations ⋮ Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy method ⋮ Solving the backward heat conduction problem by homotopy analysis method ⋮ Approximate limit cycles of coupled nonlinear oscillators with fractional derivatives ⋮ A modified numerical scheme and convergence analysis for fractional model of Lienard's equation ⋮ Analysis of large amplitude free vibrations of clamped tapered beams on a nonlinear elastic foundation ⋮ Solving a modified nonlinear epidemiological model of computer viruses by homotopy analysis method ⋮ New fractional derivatives applied to the Korteweg-de Vries and Korteweg-de Vries-Burgers equations ⋮ On the fractional Harry Dym equation ⋮ Homogeneous and heterogeneous reactions in a nanofluid flow due to a rotating disk of variable thickness using HAM ⋮ Entropy analysis and nanofluid past a double stretchable spinning disk using homotopy analysis method ⋮ A powerful approach to study the new modified coupled Korteweg-de Vries system ⋮ Modelling of fluid flow through porous media using memory approach: a review ⋮ Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method ⋮ A HAM-based wavelet approach for nonlinear ordinary differential equations ⋮ The shape effect of gold nanoparticles on squeezing nanofluid flow and heat transfer between parallel plates ⋮ A HAM-based wavelet approach for nonlinear partial differential equations: two dimensional Bratu problem as an application ⋮ A new approximate method and its convergence for a strongly nonlinear problem governing electrohydrodynamic flow of a fluid in a circular cylindrical conduit ⋮ Exact travelling wave solutions for the local fractional two-dimensional Burgers-type equations ⋮ Solving the one-loop soliton solution of the Vakhnenko equation by means of the homotopy analysis method ⋮ Solution of boundary layer problems with heat transfer by optimal homotopy asymptotic method ⋮ Improved \((G'/G)\)-expansion method for the space and time fractional foam drainage and KdV equations ⋮ Some notes on the general boundary element method for highly nonlinear problems ⋮ Analytical solutions to a generalized Drinfel'd-Sokolov equation related to DSSH and KdV6 ⋮ Uniformly valid solution of limit cycle of the Duffing-van der Pol equation ⋮ The homotopy analysis method for solving the fornberg-whitham equation and comparison with Adomian's decomposition method ⋮ Global error minimization method for solving strongly nonlinear oscillator differential equations ⋮ Solution of nonlinear fractional differential equations using homotopy analysis method ⋮ Numerical solutions of partial differential equations by discrete homotopy analysis method ⋮ Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method ⋮ A high accuracy numerical approach for electro-hydrodynamic flow of a fluid in an ion-drag configuration in a circular cylindrical conduit ⋮ Solutions for food chain ecoepidemic model with considering infection using Adomian decomposition and differential transformation methods ⋮ The homotopy analysis method for solving the time-fractional Fornberg-Whitham equation and comparison with Adomian's decomposition method ⋮ Assessment of structural health monitoring by analyzing some modal parameters (I) (an inventory of methods and some developments) ⋮ On homotopy analysis method applied to linear optimal control problems ⋮ Three-dimensional flow over a stretching surface in a viscoelastic fluid ⋮ Unsteady axisymmetric flow of a second-grade fluid over a radially stretching sheet ⋮ Comparison of HAM and HPM methods in nonlinear heat conduction and convection equations ⋮ Analytic solution of multipantograph equation ⋮ Modified Camassa-Holm and Degasperis-Procesi equations solved by Adomian's decomposition method and comparison with HPM and exact solutions ⋮ An approximation of the analytical solution of the linear and nonlinear integro-differential equations by homotopy perturbation method ⋮ MHD flow of a micropolar fluid near a stagnation-point towards a nonlinear stretching surface ⋮ Unsteady electrohydrodynamic stagnation point flow of hybrid nanofluid past a convective heated stretch/shrink sheet ⋮ Implicit differential equation arising in the steady flow of a Sisko fluid ⋮ An analytical study of boundary layer flows on a continuous stretching surface ⋮ Adomian's decomposition method and homotopy perturbation method in solving nonlinear equations ⋮ Analytic solution for axisymmetric flow over a nonlinearly stretching sheet ⋮ Analytic approximate solutions for unsteady two-dimensional and axisymmetric squeezing flows between parallel plates ⋮ Series solutions of unsteady MHD flows above a rotating disk ⋮ Purely analytic approximate solutions for steady three-dimensional problem of condensation film on inclined rotating disk by homotopy analysis method ⋮ Comparison between the homotopy analysis method and homotopy perturbation method to solve coupled Schrödinger-KdV equation ⋮ Solution of delay differential equation by means of homotopy analysis method ⋮ Series solutions of systems of nonlinear fractional differential equations ⋮ A linearization-based computational algorithm of homotopy analysis method for nonlinear reaction-diffusion systems ⋮ Direct solution of \(n\)th-order IVPs by homotopy analysis method ⋮ Heat transfer in unsteady axisymmetric second grade fluid ⋮ A symplectic homotopy perturbation method for stochastic and interval Hamiltonian systems and its applications in structural dynamic systems ⋮ The homotopy simulation of MHD time dependent three dimensional shear thinning fluid flow over a stretching plate ⋮ An optimal homotopy analysis transform method for handling nonlinear PDEs ⋮ Computational technique to study analytical solutions to the fractional modified KdV-Zakharov-Kuznetsov equation ⋮ Comparison between homotopy analysis method and homotopy renormalization method in fluid mechanics ⋮ A reliable solution of nonlinear time dependent fractional model of ebola virus disease with arbitrary order derivative in Liouville-Caputo sense ⋮ A hybrid computational scheme with convergence analysis for the dependent Rosenau-Hyman equation of arbitrary order via Caputo-Fabrizio operator ⋮ Analytical solution of hyperchaotic Zhou equations by multistage homotopy analysis method ⋮ Analytical study of \((3+1)\)-dimensional fractional-reaction diffusion trimolecular models ⋮ Numerical algorithm for solution of the system of Emden-Fowler type equations

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• A simple approach of enlarging convergence regions of perturbation approximations
• On Boundary Layers in Fluid Mechanics that Decay Algebraically along Stretches of Wall that are not Vanishingly Small
• A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate
• Analytic solutions of the temperature distribution in Blasius viscous flow problems

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