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Finding Discontinuous Solutions to the Differential-Difference Equations by the Homotopy Analysis Method |
| ZOU Li1,2,5**, ZOU Dong-Yang1,2, WANG Zhen4, ZONG Zhi2,3 |
1School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116085
2State Key Laboratory of Structure Analysis for Industrial Equipment, Dalian 116085
3School of Naval Architecture and Ocean Engineering, Dalian University of Technology, Dalian 116085
4Department of Applied Mathematics, Dalian University of Technology, Dalian 116085
5Department of Mathematics, Fluid Dynamics Group, Imperial College, London SW7 2AZ, UK
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| Cite this article: |
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ZOU Li, ZOU Dong-Yang, WANG Zhen et al 2013 Chin. Phys. Lett. 30 020204 |
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Abstract An analytic method, namely the homotopy analysis method, is applied to nonlinear problems with discontinuity governed by the differential-difference equation. Purely analytic solutions are given for nonlinear problems with discontinuity with a global convergence. This method provides a new analytical approach to solve nonlinear problems with discontinuity. Comparisons are made between the results of the proposed method and the exact solutions. The results reveal that the proposed method is very effective and convenient.
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Received: 22 July 2012
Published: 02 March 2013
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| PACS: |
02.60.Cb
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(Numerical simulation; solution of equations)
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02.60.Gf
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(Algorithms for functional approximation)
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02.60.Lj
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(Ordinary and partial differential equations; boundary value problems)
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