Finite Difference Preconditioning for Solving Orthogonal Collocation Equations for Boundary Value Problems

Authors:
Weiwei Sun;Weizhang Huang;Robert D. Russell
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
1996

Citing 0
Cited 3

A Collocation Method with Exact Imposition of Mixed Boundary Conditions

Journal of Scientific Computing
Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation

Journal of Computational Physics
Spatially Dispersionless, Unconditionally Stable FC---AD Solvers for Variable-Coefficient PDEs

Journal of Scientific Computing

Quantified Score

Hi-index	0.01

Visualization

Abstract

A technique to construct a low-order finite difference preconditioner for solving orthogonal collocation equations for boundary value problems is presented. It is shown numerically and theoretically that the spectral condition numbers of the preconditioned collocation matrices are bounded by constants independent of the number of mesh nodes when certain exact low-order finite difference preconditionings are used. Preconditioners based on incomplete LU factorization are also discussed. Numerical experiments show the efficiency and robustness of the preconditioning.