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EFFICIENT AND ACCURATE CHEBYSHEV DUAL-PETROV-GALERKIN METHODS FOR ODD-ORDER DIFFERENTIAL EQUATIONS

Xuhong Yu, Lusha Jin, Zhongqing Wang   

  1. School of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Received:2018-12-20 Revised:2019-06-03 Online:2021-01-15 Published:2021-03-11
  • Supported by:
    This work was supported by Natural Science Foundation of China (Nos. 11571238, 11601332 and 11871043).

Xuhong Yu, Lusha Jin, Zhongqing Wang. EFFICIENT AND ACCURATE CHEBYSHEV DUAL-PETROV-GALERKIN METHODS FOR ODD-ORDER DIFFERENTIAL EQUATIONS[J]. Journal of Computational Mathematics, 2021, 39(1): 43-62.

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.

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