Piecewise homotopy methods for nonlinear ordinary differential equations
From MaRDI portal
Publication:2425965
DOI10.1016/j.amc.2007.08.030zbMath1137.65048OpenAlexW2014060509MaRDI QIDQ2425965
Publication date: 17 April 2008
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2007.08.030
decomposition methodnumerical examplesvariable step sizePicard's theoremnonlinear second-order ordinary differential equationshomotopy perturbation techniquepiecewise-adaptive methods
Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05)
Related Items (9)
A non-iterative derivative-free method for nonlinear ordinary differential equations ⋮ Parametric analysis of steady bifurcations in 2D incompressible viscous flow with high order algorithm ⋮ Iterative and non-iterative methods for non-linear Volterra integro-differential equations ⋮ Convergence and error estimation of homotopy perturbation method for Fredholm and Volterra integral equations ⋮ Homotopy perturbation method and Chebyshev polynomials for solving a class of singular and hypersingular integral equations ⋮ Asymptotic expansions for the Sturm-Liouville problem by homotopy perturbation method ⋮ Modified homotopy perturbation method for solving hypersingular integral equations of the second kind ⋮ Picard's iterative method for nonlinear advection-reaction-diffusion equations ⋮ Modified homotopy perturbation method for solving fractional differential equations
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On Adomian's decomposition method and some comparisons with Picard's iterative scheme
- Non-standard, explicit integration algorithms based on linearization for nonlinear dynamic response analysis
- Linearization methods in classical and quantum mechanics
- Highly precise solutions of the one-dimensional Schrödinger equation with an arbitrary potential
- On the convergence region for decomposition solutions
- Convergent series solution of nonlinear equations
- Convergence of Adomian's method
- Numerical algorithms and decomposition
- Piecewise-linearized methods for oscillators with limit cycles
- An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude
- Piecewise-linearized methods for single degree-of-freedom problems
- Homotopy-perturbation method for pure nonlinear differential equation
- Piecewise-linearized methods for initial-value problems with oscillating solutions
- On Linstedt-Poincaré techniques for the quintic Duffing equation
- A comparison between Adomian's decomposition methods and perturbation techniques for nonlinear random differential equations
- On the Adomian (decomposition) method and comparisons with Picard's method
- Numerical integration, analytic continuation, and decomposition
- New results for convergence of Adomian's method applied to integral equations
- Noise terms in decomposition solution series
- A reliable modification of Adomian decomposition method
- A piecewise time-linearized method for the logistic differential equation
- Solving frontier problems of physics: the decomposition method
- Decomposition methods: A new proof of convergence
- The theoretical foundation of the Adomian method
- Convergence of Adomian's method applied to differential equations
- Convergence of Adomian's method applied to nonlinear equations
- Necessary conditions for the appearance of noise terms in decomposition solution series
- A mathematical model of Adomian polynomials
- Exact integration of reduced Fisher's equation, reduced Blasius equation, and the Lorenz model
- Linearization techniques for singular initial-value problems of ordinary differential equations
- Application of He's homotopy perturbation method to Volterra's integro-differential equation
- Linearized methods for ordinary differential equations
- Nonlinear equations with mixed derivatives
- The noisy convergence phenomena in decomposition method solutions
- New method for calculating Adomian polynomials
- Nonlinear stochastic differential delay equations
- A computational algebraic investigation of the decomposition method for time-dependent problems
- On the order of convergence of Adomian method.
- Homotopy perturbation method: a new nonlinear analytical technique
- A nonstandard Euler scheme for \(y+g(y)y'+f(y)y=0\)
- Asymptotology by homotopy perturbation method
- New ideas for proving convergence of decomposition methods
- Homotopy perturbation technique
- Linearized Galerkin and artificial parameter techniques for the determination of periodic solutions of nonlinear oscillators
- Application of homotopy perturbation method to nonlinear wave equations
- The decomposition method for stiff systems of ordinary differential equations
- A new algorithm for calculating Adomian polynomials
- Convergence of Adomian’s method applied to algebraic equations
- Algorithm 652
- The Cheater’s Homotopy: An Efficient Procedure for Solving Systems of Polynomial Equations
- Solving Ordinary Differential Equations I
- Application of the homotopy perturbation method to the nonlinear pendulum
- Convergence of Adomian’s method applied to integral equations
- SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS
This page was built for publication: Piecewise homotopy methods for nonlinear ordinary differential equations
