New method based on the HPM and RKHSM for solving forced Duffing equations with integral boundary conditions

Authors:
Fazhan Geng;Minggen Cui
Affiliations:
Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, China;Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong 264209, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 13
Cited 2

A parabolic equation with nonlocal boundary conditions arising from electrochemistry

Nonlinear Analysis: Theory, Methods & Applications
Weak solution to an evolution problem with a nonlocal constraint

SIAM Journal on Mathematical Analysis
Stepwise stability for the heat equation with a nonlocal constraint

SIAM Journal on Numerical Analysis
Fully implicit finite differences methods for two-dimensional diffusion with a non-local boundary condition

Journal of Computational and Applied Mathematics
Crank-Nicolson finite difference method for two-dimensional diffusion with an integral condition

Applied Mathematics and Computation
How to solve the equation AuBu + Cu = f

Applied Mathematics and Computation
Stability in the numerical solution of the heat equation with nonlocal boundary conditions

Applied Numerical Mathematics
The exact solution for solving a class nonlinear operator equations in the reproducing kernel space

Applied Mathematics and Computation
Solving singular two-point boundary value problem in reproducing kernel space

Journal of Computational and Applied Mathematics
Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations

Journal of Computational and Applied Mathematics
He's homotopy perturbation method for a boundary layer equation in unbounded domain

Computers & Mathematics with Applications
Numerical solution of one-dimensional Burgers' equation using reproducing kernel function

Journal of Computational and Applied Mathematics
Solving singular boundary-value problems of higher even-order

Journal of Computational and Applied Mathematics

Error estimation for the reproducing kernel method to solve linear boundary value problems

Journal of Computational and Applied Mathematics
A numerical method for singularly perturbed turning point problems with an interior layer

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

This paper investigates the forced Duffing equation with integral boundary conditions. Its approximate solution is developed by combining the homotopy perturbation method (HPM) and the reproducing kernel Hilbert space method (RKHSM). HPM is based on the use of the traditional perturbation method and the homotopy technique. The HPM can reduce nonlinear problems to some linear problems and generate a rapid convergent series solution in most cases. RKHSM is also an analytical technique, which can solve powerfully linear boundary value problems. Therefore, the forced Duffing equation with integral boundary conditions can be solved using advantages of these two methods. Two numerical examples are presented to illustrate the strength of the method.