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 - <p style="text-align: justify;">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.</p>