Volume 39, Issue 1
Efficient and Accurate Chebyshev Dual-Petrov-Galerkin Methods for Odd-Order Differential Equations

Xuhong Yu, Lusha Jin & Zhongqing Wang

J. Comp. Math., 39 (2021), pp. 43-62.

Published online: 2020-09

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  • Abstract

Efficient and accurate Chebyshev dual-Petrov-Galerkin methods for solving first-order equation, third-order equation, third-order KdV equation and fifth-order Kawahara equation are proposed. Some Sobolev bi-orthogonal basis functions are constructed which lead to the diagonalization of discrete systems. Accordingly, both the exact solutions and the approximate solutions are expanded as an infinite and truncated Fourier-like series, respectively. Numerical experiments illustrate the effectiveness of the suggested approaches.

  • Keywords

Chebyshev dual-Petrov-Galerkin method, Sobolev bi-orthogonal polynomials, odd-order differential equations, Numerical results.

  • AMS Subject Headings

65N35, 33C45, 35J58

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xhyu@usst.edu.cn (Xuhong Yu)

ls.jin@foxmail.com (Lusha Jin)

zqwang@usst.edu.cn (Zhongqing Wang)

  • BibTex
  • RIS
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@Article{JCM-39-43, author = {Yu , Xuhong and Jin , Lusha and Wang , Zhongqing }, title = {Efficient and Accurate Chebyshev Dual-Petrov-Galerkin Methods for Odd-Order Differential Equations}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {39}, number = {1}, pages = {43--62}, abstract = {

Efficient and accurate Chebyshev dual-Petrov-Galerkin methods for solving first-order equation, third-order equation, third-order KdV equation and fifth-order Kawahara equation are proposed. Some Sobolev bi-orthogonal basis functions are constructed which lead to the diagonalization of discrete systems. Accordingly, both the exact solutions and the approximate solutions are expanded as an infinite and truncated Fourier-like series, respectively. Numerical experiments illustrate the effectiveness of the suggested approaches.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1907-m2018-0285}, url = {http://global-sci.org/intro/article_detail/jcm/18277.html} }
TY - JOUR T1 - Efficient and Accurate Chebyshev Dual-Petrov-Galerkin Methods for Odd-Order Differential Equations AU - Yu , Xuhong AU - Jin , Lusha AU - Wang , Zhongqing JO - Journal of Computational Mathematics VL - 1 SP - 43 EP - 62 PY - 2020 DA - 2020/09 SN - 39 DO - http://doi.org/10.4208/jcm.1907-m2018-0285 UR - https://global-sci.org/intro/article_detail/jcm/18277.html KW - Chebyshev dual-Petrov-Galerkin method, Sobolev bi-orthogonal polynomials, odd-order differential equations, Numerical results. AB -

Efficient and accurate Chebyshev dual-Petrov-Galerkin methods for solving first-order equation, third-order equation, third-order KdV equation and fifth-order Kawahara equation are proposed. Some Sobolev bi-orthogonal basis functions are constructed which lead to the diagonalization of discrete systems. Accordingly, both the exact solutions and the approximate solutions are expanded as an infinite and truncated Fourier-like series, respectively. Numerical experiments illustrate the effectiveness of the suggested approaches.

Xuhong Yu, Lusha Jin & Zhongqing Wang. (2020). Efficient and Accurate Chebyshev Dual-Petrov-Galerkin Methods for Odd-Order Differential Equations. Journal of Computational Mathematics. 39 (1). 43-62. doi:10.4208/jcm.1907-m2018-0285
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