On the variational iteration method and other iterative techniques for nonlinear differential equations
DOI10.1016/j.amc.2007.09.024zbMath1142.65082OpenAlexW2045010625MaRDI QIDQ924379
Publication date: 16 May 2008
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2007.09.024
convergenceFredholm integral equationsGreen's functionnumerical examplesiterative methodsmethod of weighted residualsVolterra integral equationinitial-value problemsboundary-value problemsadjoint operatorvariational iteration methodBellman-Kalaba quasilinearization techniqueLagrange density
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) Initial value problems for nonlinear higher-order PDEs (35G25) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Variational iteration method for solving Burgers and coupled Burgers equations
- Quantitative measurement of variational approximations
- Application of He's variational iteration method to Helmholtz equation
- Comparison of quasilinear and WKB approximations
- Variational iteration method -- a kind of non-linear analytical technique: Some examples
- Modified Lindstedt-Poincaré methods for some strongly nonlinear oscillations. I: Expansion of a constant
- Analytical approximation to large-amplitude oscillation of a non-linear conservative system
- An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude
- Large amplitude non-linear oscillations of a general conservative system
- Series approach to the Lane-Emden equation and comparison with the homotopy perturbation method
- Variational theory for one-dimensional longitudinal beam dynamics
- On Linstedt-Poincaré techniques for the quintic Duffing equation
- He's parameter-expanding methods for strongly nonlinear oscillators
- An analytical approximate technique for a class of strongly non-linear oscillators
- Solving frontier problems of physics: the decomposition method
- Variational approach to the Thomas-Fermi equation
- Variational approach to the sixth-order boundary value problems
- Variational approach to the Lane--Emden equation
- A Lagrangian for von Kármán equations of large deflection problem of thin circular plate.
- Presenting a new method for the solution of nonlinear problems
- Harmonic balance based averaging: Approximate realizations of an asymptotic technique
- Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt--Poincaré method
- Nonlinear equations with mixed derivatives
- Nonlinear stochastic differential delay equations
- Homotopy perturbation method: a new nonlinear analytical technique
- A new analytical approach to the Duffing-harmonic oscillator
- Multiple scale and singular perturbation methods
- Homotopy perturbation technique
- Numerical comparison of methods for solving linear differential equations of fractional order
- High order analysis of nonlinear periodic differential equations
- Variational iteration method for one-dimensional nonlinear thermoelasticity
- Comparison of alternative improved perturbative methods for nonlinear oscillations
- Construction of solitary solution and compacton-like solution by variational iteration method
- A numerical simulation and explicit solutions of KdV-Burgers' and Lax's seventh-order KdV equations
- The solution of nonlinear coagulation problem with mass loss
- A modified iteration perturbation method for some nonlinear oscillation problems
- New applications of variational iteration method
- Iteration procedure for determining approximate solutions to non-linear oscillator equations
- A classical perturbation technique that works even when the linear part of restoring force is zero
- A modified method of equivalent linearization that works even when the non-linearity is not small
- Comparison of two Lindstedt–Poincaré-type perturbation methods
- MATHEMATICAL AND NUMERICAL STUDY OF THE DUFFING-HARMONIC OSCILLATOR
- OSCILLATIONS IN AN x4/3POTENTIAL
- ANALYSIS OF NON-LINEAR OSCILLATORS HAVING NON-POLYNOMIAL ELASTIC TERMS
- MODIFIED MICKENS PROCEDURE FOR CERTAIN NON-LINEAR OSCILLATORS
- A qualitative study of the solutions to the differential equation
- Improved Lindstedt–Poincaré method for the solution of nonlinear problems
- Analytical study on a Duffing-harmonic oscillator
- A convolution integral method for certain strongly nonlinear oscillators
- A classical iteration procedure valid for certain strongly nonlinear oscillators
- Asymptotic representations of the period for the nonlinear oscillator
- Development of accurate solutions for a classical oscillator
- Determination of periodic solution for a u1/3 force by He's modified Lindstedt–Poincaré method
- Erratum to “Asymptotic representations of the period for the nonlinear oscillator <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo>¨</mml:mo></mml:mover></mml:mrow><mml:mo>+</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo>˙</mml:mo>
- A generalized iteration procedure for calculating approximations to periodic solutions of “truly nonlinear oscillators”
- Iteration method solutions for conservative and limit-cycle force oscillators
- Investigation of the properties of the period for the nonlinear oscillator
- Solutions of nonlinear oscillators with fractional powers by an iteration procedure
- Solution of a Duffing-harmonic oscillator by the method of harmonic balance
- Higher accuracy analytical approximations to the Duffing-harmonic oscillator
- Solutions of the Duffing-harmonic oscillator by an iteration procedure
- Computational Methods for Integral Equations
- Perturbation methods and non-linear hyperbolic waves
- A Perturbation Technique that Works Even When the Non-Linearity is Not Small
- Finitely-generated solutions of certain integral equations
- A new perturbative approach to nonlinear problems
- SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS
- A new approach to nonlinear partial differential equations
- Variational iteration method for autonomous ordinary differential systems
- Numerical investigation of quasilinearization method in quantum mechanics
- Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs
- A method for obtaining approximate analytic periods for a class of nonlinear oscillators
This page was built for publication: On the variational iteration method and other iterative techniques for nonlinear differential equations