Iterative Multistep Reproducing Kernel Hilbert Space Method for Solving Strongly Nonlinear Oscillators
Open Access
- 17 June 2014
- journal article
- research article
- Published by Hindawi Limited in Advances in Mathematical Physics
- Vol. 2014 (3), 1-7
- https://doi.org/10.1155/2014/758195
Abstract
A new algorithm called multistep reproducing kernel Hilbert space method is represented to solve nonlinear oscillators models. The proposed scheme is a modification of the reproducing kernel Hilbert space method, which will increase the intervals of convergence for the series solution. The numerical results demonstrate the validity and the applicability of the new technique. A very good agreement was found between the results obtained using the presented algorithm and the Runge-Kutta method, which shows that the multistep reproducing kernel Hilbert space method is very efficient and convenient for solving nonlinear oscillators models.Keywords
This publication has 17 references indexed in Scilit:
- Solving Fredholm integro–differential equations using reproducing kernel Hilbert space methodApplied Mathematics and Computation, 2013
- A Reproducing Kernel Hilbert Space Method for Solving Integro-Differential Equations of Fractional OrderJournal of Optimization Theory and Applications, 2012
- Solving singular second-orderinitial/boundary value problems in reproducing kernel Hilbert spaceBoundary Value Problems, 2012
- Differential transformation method for solving one-space-dimensional telegraph equationComputational and Applied Mathematics, 2011
- The modified homotopy perturbation method for solving strongly nonlinear oscillatorsComputers & Mathematics with Applications, 2009
- An artificial parameter-decomposition method for nonlinear oscillators: Applications to oscillators with odd nonlinearitiesJournal of Sound and Vibration, 2007
- Solving singular two-point boundary value problem in reproducing kernel spaceJournal of Computational and Applied Mathematics, 2007
- Solving a nonlinear system of second order boundary value problemsJournal of Mathematical Analysis and Applications, 2007
- ANALYTICAL APPROXIMATE SOLUTIONS OF NONLINEAR OSCILLATORS BY THE MODIFIED DECOMPOSITION METHODInternational Journal of Modern Physics C, 2004
- PERIODIC SOLUTIONS OF STRONGLY NON-LINEAR OSCILLATORS BY THE MULTIPLE SCALES METHODJournal of Sound and Vibration, 2002