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Volume 9, Issue 4
A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

Zhongqing Wang & Jun Mu

DOI: 10.4208/nmtma.2016.m1429

Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 619-639.

Published online: 2016-09

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  • Abstract

We introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain the $hp$-version bound on the numerical error of the multiple interval collocation method under $H^1$-norm. Numerical experiments confirm the theoretical expectations.

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@Article{NMTMA-9-619, author = {Zhongqing Wang and Jun Mu}, title = {A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations }, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2016}, volume = {9}, number = {4}, pages = {619--639}, abstract = {

We introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain the $hp$-version bound on the numerical error of the multiple interval collocation method under $H^1$-norm. Numerical experiments confirm the theoretical expectations.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2016.m1429}, url = {http://global-sci.org/intro/article_detail/nmtma/12392.html} }
TY - JOUR T1 - A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations AU - Zhongqing Wang & Jun Mu JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 619 EP - 639 PY - 2016 DA - 2016/09 SN - 9 DO - http://doi.org/10.4208/nmtma.2016.m1429 UR - https://global-sci.org/intro/article_detail/nmtma/12392.html KW - AB -

We introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain the $hp$-version bound on the numerical error of the multiple interval collocation method under $H^1$-norm. Numerical experiments confirm the theoretical expectations.

Zhongqing Wang and Jun Mu. (2016). A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations . Numerical Mathematics: Theory, Methods and Applications. 9 (4). 619-639. doi:10.4208/nmtma.2016.m1429
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