An effective modification of the homotopy perturbation method for stiff systems of ordinary differential equations

DOI10.1016/j.aml.2011.03.032zbMath1220.34012OpenAlexW2083845046MaRDI QIDQ548398

Hossein Aminikhah, Milad Hemmatnezhad

Publication date: 28 June 2011

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2011.03.032

zbMATH Keywords

stiff problemshomotopy perturbation methodlinear and nonlinear ODEs

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Theoretical approximation of solutions to ordinary differential equations (34A45) Numerical methods for stiff equations (65L04)

Related Items

Numerical solution of fractional partial differential equations by numerical Laplace inversion technique ⋮ Dynamic model of large amplitude non-linear oscillations arising in the structural engineering: analytical solutions ⋮ Exploring the novel continuum-cancellation Leal-method for the approximate solution of nonlinear differential equations ⋮ Application of the homotopy perturbation method to an inverse heat problem ⋮ An accurate block solver for stiff initial value problems ⋮ Construction of fractional power series solutions to fractional stiff system using residual functions algorithm ⋮ A family of matrix coefficient formulas for solving ordinary differential equations ⋮ Modified reduced differential transform method for partial differential-algebraic equations ⋮ Rational homotopy perturbation method for solving stiff systems of ordinary differential equations ⋮ A new variable step size block backward differentiation formula for solving stiff initial value problems

Cites Work

• Unnamed Item
• Exact solutions for non-linear Schrödinger equations by He's homotopy perturbation method
• The numerical simulation for stiff systems of ordinary differential equations
• Modified homotopy perturbation method for solving Fredholm integral equations
• Recent development of the homotopy perturbation method
• Solution of delay differential equations via a homotopy perturbation method
• He's variational iteration method for solving linear and non-linear systems of ordinary differential equations
• Application of homotopy perturbation method for solving eighth-order boundary value problems
• Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations
• Homotopy perturbation method for solving hyperbolic partial differential equations
• Four-step exponential-fitted methods for nonlinear physical problems
• Solution of the system of ordinary differential equations by Adomian decomposition method.
• The homotopy perturbation method for nonlinear oscillators with discontinuities.
• Frequency evaluation in exponential fitting multistep algorithms for ODEs
• Homotopy perturbation method for solving boundary value problems
• Homotopy perturbation technique
• The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer
• Application of He's homotopy perturbation method to conservative truly nonlinear oscillators
• Comparison of some recent numerical methods for initial-value problems for stiff ordinary differential equations
• Homotopy perturbation method for thin film flow of a third-grade fluid down an inclined plane
• Limit cycle and bifurcation of nonlinear problems
• Application of homotopy perturbation method to nonlinear wave equations
• Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order
• AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING
• The solution of a combustion problem with Rosenbrock methods
• SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS