تقرير
A $\star$-product solver with spectral accuracy for non-autonomous ordinary differential equations
| العنوان: | A $\star$-product solver with spectral accuracy for non-autonomous ordinary differential equations |
|---|---|
| المؤلفون: | Pozza, Stefano, Van Buggenhout, Niel |
| سنة النشر: | 2022 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 34A30, 41A10, 65L05 |
| الوصف: | A new method for solving non-autonomous ordinary differential equations is proposed, the method achieves spectral accuracy. It is based on a new result which expresses the solution of such ODEs as an element in the so called $\star$-algebra. This algebra is equipped with a product, the $\star$-product, which is the integral over the usual product of two bivariate distributions. Expanding the bivariate distributions in bases of Legendre polynomials leads to a discretization of the $\star$-product and this allows for the solution to be approximated by a vector that is obtained by solving a linear system of equations. The effectiveness of this approach is illustrated with numerical experiments. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2209.15533 |
| رقم الأكسشن: | edsarx.2209.15533 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |