A fast and well-conditioned spectral method

Details A fast and well-conditioned spectral method A fast and well-conditioned spectral method

2012-02-07

arxiv.org/abs/1202.1347v1

Mathematics

Numerical Analysis

Scientific paper

A novel spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n) operations, where m is the number of Chebyshev points needed to resolve the coefficients of the differential operator and n is the number of Chebyshev points needed to resolve the solution to the differential equation. We prove stability of the method by relating it to a diagonally preconditioned system which has a bounded condition number, in a suitable norm. For Dirichlet boundary conditions, this reduces to stability in the standard 2-norm.

Affiliated with

Also associated with

No associations

Rating

A fast and well-conditioned spectral method does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A fast and well-conditioned spectral method, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A fast and well-conditioned spectral method will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-578845