Efficient and Accurate Chebyshev Dual-Petrov-Galerkin Methods for Odd-Order Differential Equations (Journal of Computational Mathematics, 2021)
Efficient and accurate Chebyshev dual-Petrov-Galerkin methods for solving first-orderequation, third-order equation, third-order KdV equation and fifth-order Kawahara equation are proposed. Some Sobolev bi-orthogonal basis functions are constructed which leadto the diagonalization of discrete systems. Accordingly, both the exact solutions and theapproximate 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.