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.