Investigating the solutions of two classical nonlinear oscillators by the AG method

DOI10.1007/s40819-021-00985-9zbMath1506.70030OpenAlexW3163975367MaRDI QIDQ2114764

Amirreza Lashkarboluki, Hamed Hosseini, Davood Dimiri Ganji

Publication date: 15 March 2022

Published in: International Journal of Applied and Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40819-021-00985-9

zbMATH Keywords

algebraic methodvariational iteration methodenergy balance methodGaylord oscillatorparameterized perturbation methodtwo-spring oscillator

Mathematics Subject Classification ID

General perturbation schemes for nonlinear problems in mechanics (70K60) Computational methods for problems pertaining to mechanics of particles and systems (70-08)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Application of optimal homotopy asymptotic method for the analytic solution of singular Lane-Emden type equation
• Variational iteration method for solving Burgers and coupled Burgers equations
• Accurate analytical solutions to oscillators with discontinuities and fractional-power restoring force by means of the optimal homotopy asymptotic method
• Application of homotopy analysis method to the unsteady squeezing flow of a second-grade fluid between circular plates
• Nonlinear vibration analysis of a rigid rod on a circular surface via Hamiltonian approach
• A new homotopy perturbation method for solving systems of partial differential equations
• He's homotopy perturbation method for systems of integro-differential equations
• The variational iteration method for fourth order boundary value problems
• Effects of variable viscosity in a third grade fluid with porous medium: an analytic solution
• An optimal homotopy-analysis approach for strongly nonlinear differential equations
• Application of He's variational iteration method to Helmholtz equation
• Homotopy perturbation method for Fangzhu oscillator
• Variational iteration method -- a kind of non-linear analytical technique: Some examples
• Solution of the epidemic model by homotopy perturbation method
• Analytical solution of the Klein-Gordon equation by a new homotopy perturbation method
• New homotopy perturbation method for a special kind of Volterra integral equations in two-dimensional space
• Variational iteration method: New development and applications
• The variational iteration method: A reliable analytic tool for solving linear and nonlinear wave equations
• He's variational iteration method for fourth-order parabolic equations
• Periodic solutions for some strongly nonlinear oscillations by He's variational iteration method
• A study on linear and nonlinear Schrödinger equations by the variational iteration method
• The application of homotopy analysis method to nonlinear equations arising in heat transfer
• Recent development of the homotopy perturbation method
• A reliable treatment of a homotopy analysis method for two-dimensional viscous flow in a rectangular domain bounded by two moving porous walls
• Variational iteration method for unsteady flow of gas through a porous medium using He's polynomials and Padé approximants
• Some solutions of the linear and nonlinear Klein-Gordon equations using the optimal homotopy asymptotic method
• Application of homotopy perturbation method for solving eighth-order boundary value problems
• Variational iteration method -- some recent results and new interpretations
• The variational iteration method for rational solutions for KdV, \(K(2,2)\), Burgers, and cubic Boussinesq equations
• Application of He's variational iteration method to nonlinear Jaulent-Miodek equations and comparing it with ADM
• A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials
• Modified variational iteration method for heat and wave-like equations
• The variational iteration method for analytic treatment for linear and nonlinear ODEs
• Purely analytic approximate solutions for steady three-dimensional problem of condensation film on inclined rotating disk by homotopy analysis method
• Application of he's homotopy perturbation method for solving the Cauchy reaction-diffusion problem
• A new modification of He's homotopy perturbation method for rapid convergence of nonlinear undamped oscillators
• An approximate solution technique depending on an artificial parameter: A special example
• Homotopy analysis method: A new analytical technique for nonlinear problems
• Solving frontier problems of physics: the decomposition method
• Variational approach to the Thomas-Fermi equation
• The homotopy perturbation method for nonlinear oscillators with discontinuities.
• A coupling method of a homotopy technique and a perturbation technique for nonlinear problems
• The optimal homotopy asymptotic method for solving Blasius equation
• Investigation on non-linear vibration in arched beam for bridges construction via AGM method
• Laplace transform: making the variational iteration method easier
• Solving a system of linear and nonlinear fractional partial differential equations using homotopy perturbation method
• Approximate analytical solution for seepage flow with fractional derivatives in porous media
• Preliminary report on the energy balance for nonlinear oscillations.
• Modified variational iteration method (non-homogeneous initial value problem)
• Analytical solution to nonlinear oscillation system of the motion of a rigid rod rocking back using max-min approach
• Homotopy perturbation method for solving boundary value problems
• Homotopy perturbation technique
• A fractal Boussinesq equation for nonlinear transverse vibration of a nanofiber-reinforced concrete pillar
• Generalized variational principles for buckling analysis of circular cylinders
• Analytical approach to linear fractional partial differential equations arising in fluid mechanics
• The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer
• Study of convergence of homotopy perturbation method for two-dimensional linear Volterra integral equations of the first kind
• The variational iteration method for solving two forms of Blasius equation on a half-infinite domain
• Variational iteration method for solving wave equation
• Application of He's homotopy perturbation method to conservative truly nonlinear oscillators
• A generalized variational principle in micromorphic thermoelasticity
• Construction of solitary solution and compacton-like solution by variational iteration method
• The solution of nonlinear coagulation problem with mass loss
• Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order
• An efficient method for Cauchy problem of ill‐posed nonlinear diffusion equation
• An analytic solution of micropolar flow in a porous channel with mass injection using homotopy analysis method
• An efficient analytic approach for solving two-point nonlinear boundary value problems by homotopy analysis method
• A new technique of using homotopy analysis method for solving high-order nonlinear differential equations
• HE'S ITERATION PERTURBATION METHOD TO NONLINEAR OSCILLATIONS OF MECHANICAL SYSTEMS WITH SINGLE-DEGREE-OF FREEDOM
• Solution of the wave equation by homotopy perturbation method
• NEW ANALYTICAL SOLUTION OF THE THREE-DIMENSIONAL NAVIER–STOKES EQUATIONS
• Beyond Perturbation
• On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet
• Solving nonlinear fractional partial differential equations using the homotopy analysis method
• Approximate solution of two-term fractional-order diffusion, wave-diffusion, and telegraph models arising in mathematical physics using optimal homotopy asymptotic method
• The variational iteration method for eighth-order initial-boundary value problems
• SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS
• A new approach to nonlinear partial differential equations
• Variational iteration method for autonomous ordinary differential systems
• The reducing rank method to solve third‐order Duffing equation with the homotopy perturbation