Homotopy perturbation method: a new nonlinear analytical technique

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DOI10.1016/S0096-3003(01)00312-5zbMath1030.34013OpenAlexW2003806194MaRDI QIDQ1855964

Publication date: 28 January 2003

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

Full work available at URL: https://doi.org/10.1016/s0096-3003(01)00312-5

zbMATH Keywords

Duffing equation

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Numerical methods for ordinary differential equations (65L99) Asymptotic theory for ordinary differential equations (34E99)

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Liouville-Caputo sense ⋮ Application of the homotopy perturbation method for the Fokker-Planck equation ⋮ A spectral element approach for the stability of delay systems ⋮ The variational iteration method for solving two forms of Blasius equation on a half-infinite domain ⋮ Application of He's homotopy perturbation method to nonlinear integro-differential equations ⋮ A new technique of using homotopy analysis method for solving high-order nonlinear differential equations ⋮ A closed-form approximation for the fractional Black-Scholes model with transaction costs ⋮ Approximations of the nonlinear Volterra's population model by an efficient numerical method ⋮ Fixed-term homotopy ⋮ A class of solvable coupled nonlinear oscillators with amplitude independent frequencies ⋮ A new algorithm for solving differential equations ⋮ Compact structures in a class of nonlinearly dispersive equations with time-fractional derivatives ⋮ A non-iterative derivative-free method for nonlinear ordinary differential equations ⋮ Homotopy analysis method for limit cycle flutter of airfoils ⋮ Numerical solution of two-dimensional nonlinear differential equation by homotopy perturbation method ⋮ An efficient algorithm for solving Troesch's problem ⋮ A new modification of the homotopy perturbation method for linear and nonlinear operators ⋮ He's homotopy perturbation method for solving the shock wave equation ⋮ Derivation of the Adomian decomposition method using the homotopy analysis method ⋮ Solution of BVPs for fourth-order integro-differential equations by using homotopy perturbation method ⋮ NUMERICAL SOLUTIONS OF WAVE EQUATIONS SUBJECT TO AN INTEGRAL CONSERVATION CONDITION BY HE'S HOMOTOPY PERTURBATION METHOD ⋮ Solutions of integral and integro-differential equation systems by using differential transform method ⋮ NUMERICAL SOLUTIONS FOR THE NONLINEAR FORNBERG–WHITHAM EQUATION BY HE'S METHODS ⋮ Convergence of the variational iteration method for solving linear systems of ODEs with constant coefficients ⋮ Application of variational iteration method and homotopy perturbation method to the modified Kawahara equation ⋮ Imposing boundary conditions in Sinc method using highest derivative approximation ⋮ Iterative and non-iterative methods for non-linear Volterra integro-differential equations ⋮ Numerical study of Burgers-Huxley equations via reduced differential transform method ⋮ Method for solving nonlinear initial value problems by combining homotopy perturbation and reproducing kernel Hilbert space methods ⋮ Remarks on the homotopy perturbation method for the peristaltic flow of Jeffrey fluid with nano-particles in an asymmetric channel ⋮ Homotopy analysis method for oscillatory systems with cubic and trigonometric non-linearity ⋮ A hybrid asymptotic and augmented compact finite volume method for nonlinear singular two point boundary value problems ⋮ A hybrid computational approach for Klein-Gordon equations on Cantor sets ⋮ On the utility of the homotopy analysis method for non-analytic and global solutions to nonlinear differential equations ⋮ A fractional order approach to modeling and simulations of the novel COVID-19 ⋮ An efficient approach for solution of fractional-order Helmholtz equations ⋮ Mixed convection fluid flow over a vertical cone saturated porous media with double dispersion and injection/suction effects ⋮ Optimal homotopy analysis and control of error for implicitly defined fully nonlinear differential equations ⋮ Application of relative entropy theory to streamwise velocity profile in open-channel flow: effect of prior probability distributions ⋮ Analysis of fractional thin film flow of third grade fluid in lifting and drainage via homotopy perturbation procedure ⋮ Numerical simulation of the Lorenz-type chaotic system using barycentric Lagrange interpolation collocation method ⋮ Application of He's homotopy perturbation method to functional integral equations ⋮ Piecewise homotopy methods for nonlinear ordinary differential equations ⋮ Lie symmetry analysis and conservation laws for the time fractional generalized advection-diffusion equation ⋮ Oxygen diffusion in a spherical cell subject to nonlinear Michaelis–Menten kinetics: Mathematical analysis by two exact methods ⋮ Eventual periodicity of forced oscillations of the Korteweg-de Vries type equation ⋮ Numerical solutions of time‐fractional Burgers equations ⋮ Peaceman‐Rachford ADI scheme for the two dimensional flow of a second‐grade fluid ⋮ Application of semi‐analytical methods for solving the Rosenau‐Hyman equation arising in the pattern formation in liquid drops ⋮ Homotopy analysis method for the one‐dimensional hyperbolic telegraph equation with initial conditions ⋮ Solution of the heat equation in the cast‐mould heterogeneous domain using a weighted algorithm based on the homotopy perturbation method ⋮ Analytical solutions to a fractional generalized two phase Lame-Clapeyron-Stefan problem ⋮ New travelling wave solutions for coupled fractional variant Boussinesq equation and approximate long water wave equation ⋮ Approximate solutions of multi-order fractional advection-dispersion equation with non-polynomial conditions ⋮ Analog circuit optimization on basis of control theory approach ⋮ Solution of the steady thin film flow of non-Newtonian fluid on vertical cylinder using Adomian decomposition method ⋮ Crack identification of beam structures using homotopy continuation algorithm ⋮ Analysis of the new homotopy perturbation method for linear and nonlinear problems ⋮ A comparison of two formulations of the fin efficiency for straight fins ⋮ Second-order two-point boundary value problems using the variational iteration algorithm-II ⋮ MODIFIED HOMOTOPY PERTURBATION METHOD FOR SOLVING INTEGRAL EQUATIONS ⋮ Theory and computation in singular boundary value problems ⋮ Thin film flow of non-Newtonian fluids on a moving belt ⋮ Numerical solution for special nonlinear Fredholm integral equation by HPM ⋮ Homotopy perturbation method for thin film flow of a third-grade fluid down an inclined plane ⋮ Dynamical behavior in the perturbed compound KdV-Burgers equation ⋮ Asymptotic numerical method for multi-degree-of-freedom nonlinear dynamic systems ⋮ Linearized Galerkin and artificial parameter techniques for the determination of periodic solutions of nonlinear oscillators ⋮ The secant-homotopy continuation method ⋮ Numerical solutions of highly oscillatory integrals ⋮ One-step recursive method for solving systems of differential equations ⋮ Nonlinear dynamic analysis of an unbalanced rotor supported by roller bearing ⋮ Limit cycle and bifurcation of nonlinear problems ⋮ The inverse kinematics problem of spatial 4P3R robot manipulator by the homotopy continuation method with an adjustable auxiliary homotopy function ⋮ An analytical approximation for solving nonlinear Blasius equation by NHPM ⋮ Analytical solutions to nonlinear equations arising in heat transfer by variational iteration, homotopy perturbation, and Adomian decomposition methods ⋮ Application of adapted homotopy perturbation method for approximate solution of Henon-Heiles system ⋮ Application of homotopy perturbation method to multidimensional partial differential equations ⋮ Periodic solution of the Duffing-Van der Pol oscillator by homotopy perturbation method ⋮ Homotopy perturbation method to obtain exact special solutions with solitary patterns for Boussinesq-like B(m,n) equations with fully nonlinear dispersion ⋮ He's homotopy perturbation method for solving the space- and time-fractional telegraph equations ⋮ Generalized homotopy method for solving nonlinear differential equations ⋮ The homotopy perturbation method for the Black–Scholes equation ⋮ Homotopy analysis method for the sine-Gordon equation with initial conditions ⋮ Variational iteration method for inverse problem of diffusion equation ⋮ Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order ⋮ Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates ⋮ Exact solutions for some systems of PDEs by He's homotopy perturbation method ⋮ Analytical Solution of the Effect of Awareness Program by Media on the Spread of an Infectious Disease by Homotopy Perturbation Method ⋮ SOLUTIONS OF HELMHOLTZ EQUATIONS BY VARIATIONAL ITERATION METHOD ⋮ The numerical solution of the second Painlevé equation ⋮ ANALYTICAL SOLUTION OF THE MAGNETO-HYDRODYNAMIC FLOW OVER A NONLINEAR STRETCHING SHEET ⋮ Analytical solution of time-fractional Navierâ Stokes equation in polar coordinate by homotopy perturbation method ⋮ APPROXIMATE SOLUTIONS OF NONLINEAR DIFFERENTIAL DIFFERENCE EQUATIONS ⋮ Analytical approach to fractional partial differential equations in fluid mechanics by means of the homotopy perturbation method ⋮ Homotopy perturbation method for numerical solutions of coupled Burgers equations with time‐ and space‐fractional derivatives ⋮ Analytical solution of wave system in Rⁿwith coupling controllers ⋮ A numerical simulation of modified Boussinesq and seven‐order Sawada‐Kotara equations ⋮ New Analytical Solution of Two-Dimensional Viscous Flow in a Rectangular Domain Bounded by Two Moving Porous Walls ⋮ A study of convergence on the Newton-homotopy continuation method ⋮ Homotopy Perturbation Algorithm Using Laplace Transform for Gas Dynamics Equation

Cites Work

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