Satisfaction of boundary conditions for Chebyshev collocation methods in cuboidal domains

Efficient Embedded Formula for Chebyshev Collocation Methods

In this talk, we are concerned with embedded formulae of the Chebyshev collocation methods [1] developed recently. We introduce two Chebyshev collocation methods based on generalized Chebyshev interpolation polynomials [2], which are used to make an automatic integration method. We apply an elegant algorithm of generalized Chebyshev interpolation increasing the node points to make an error esti...

Generalized Chebyshev Collocation Method

In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower deg...

Preconditioned Chebyshev collocation methods and triangular finite elements

This paper analyzes triangular finite elements for the preconditioning of Chebyshev collocation solutions of elliptic boundary value problems. Results are given for scalar model problems and for both Stokes and Navier-Stokes equations.

Collocation for High-Order Differential Equations with Lidstone Boundary Conditions

Fast Algorithms for Spectral Collocation with Non-Periodic Boundary Conditions

Fast Algorithms with Applications to PDEs