A Legendre-Petrov-Galerkin and Chebyshev collocation method for third-order differential equations
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
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Detail(s)
| Original language | English |
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| Pages (from-to) | 01425-1438 |
| Journal / Publication | SIAM Journal on Numerical Analysis |
| Volume | 38 |
| Issue number | 5 |
| Publication status | Published - 2001 |
Link(s)
| Attachment(s) | Documents
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| Link to Scopus | https://www.scopus.com/record/display.uri?eid=2-s2.0-0034543430&origin=recordpage |
| Permanent Link | https://scholars.cityu.edu.hk/en/publications/publication(0fad5707-8a35-4491-84f6-cf3932bcfd5d).html |
Abstract
A Legendre-Petrov-Galerkin (LPG) method for the third-order differential equation is developed. By choosing appropriate base functions, the method can be implemented efficiently. Also, this new approach enables us to derive an optimal rate of convergence in L2-norm. The method is applied to some nonlinear problems such as the Korteweg-de Vries (KdV) equation with the Chebyshev collocation treatment for the nonlinear term. It is a Legendre-Petrov-Galerkin and Chebyshev collocation (LPG-CC) method. Numerical experiments are given to confirm the theoretical result.
Research Area(s)
- Korteweg-de Vries equation, Legendre-Petrov-Galerkin and Chebyshev collocation, Third-order differential equation
Citation Format(s)
A Legendre-Petrov-Galerkin and Chebyshev collocation method for third-order differential equations. / Ma, Heping; Sun, Weiwei.
In: SIAM Journal on Numerical Analysis, Vol. 38, No. 5, 2001, p. 01425-1438.
In: SIAM Journal on Numerical Analysis, Vol. 38, No. 5, 2001, p. 01425-1438.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
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