Spectral Integration and Two-Point Boundary Value Problems
YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE
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A numerical method for two-point boundary value problems with constant coefficients is developed which is based on integral equations and the spectral integration matrix for Chebyshev nodes. The method is stable, achieves superalgebraic convergence, and requires ON log N operations, where N is the number of nodes in the discretization. Although stable spectral methods have been constructed in the past, they have generally been based on reformulating the recurrence relations obtained through spectral differentiation in an attempt to avoid the ill-conditioning introduced by that process. Keywords Differential equations, Spectral methods, Quadrature, Chebyshev polynomials, Approximation theory, Algorithms.
- Numerical Mathematics