Symmetrization of the Sinc-Galerkin method for boundary value problems
Mathematics of Computation
SPOA VII Proceedings of the seventh Spanish symposium on Orthogonal polynomials and applications
Interpolatory quadrature formulae with Chebyshev abscissae of the third or fourth kind
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Spline collocation method for solving linear sixth-order boundary-value problems
International Journal of Computer Mathematics
Efficient multi-dimensional solution of PDEs using Chebyshev spectral methods
Journal of Computational Physics
An Alternating-Direction Sinc-Galerkin method for elliptic problems
Journal of Complexity
Mathematics and Computers in Simulation
A Jacobi-Jacobi dual-Petrov-Galerkin method for third- and fifth-order differential equations
Mathematical and Computer Modelling: An International Journal
Journal of Computational Physics
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This paper is concerned with spectral Galerkin algorithms for solving high even-order two point boundary value problems in one dimension subject to homogeneous and nonhomogeneous boundary conditions. The proposed algorithms are extended to solve two-dimensional high even-order differential equations. The key to the efficiency of these algorithms is to construct compact combinations of Chebyshev polynomials of the third and fourth kinds as basis functions. The algorithms lead to linear systems with specially structured matrices that can be efficiently inverted. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithms, and some comparisons with some other methods are made.