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Univariate modified Fourier methods for second order boundary value problems
| Content Provider | Semantic Scholar |
|---|---|
| Author | Adcock, Ben |
| Copyright Year | 2009 |
| Abstract | AbstractWe develop and analyse a new spectral-Galerkin method for the numerical solution of linear, second order differential equations with homogeneous Neumann boundary conditions. The basis functions for this method are the eigenfunctions of the Laplace operator subject to these boundary conditions. Due to this property this method has a number of beneficial features, including an $\mathcal{O}(N^{2})$ condition number and the availability of an optimal, diagonal preconditioner. This method offers a uniform convergence rate of $\mathcal{O}(N^{-3})$ , however we show that by the inclusion of an additional 2M basis functions, this figure can be increased to $\mathcal{O}(N^{-2M-3})$ for any positive integer M. |
| Starting Page | 249 |
| Ending Page | 280 |
| Page Count | 32 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s10543-009-0224-1 |
| Volume Number | 49 |
| Alternate Webpage(s) | http://benadcock.org/wp-content/uploads/2015/11/AdcockUVMF.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s10543-009-0224-1 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
