تقرير
A Bernoulli-barycentric rational matrix collocation method with preconditioning for a class of evolutionary PDEs
| العنوان: | A Bernoulli-barycentric rational matrix collocation method with preconditioning for a class of evolutionary PDEs |
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| المؤلفون: | Luo, Wei-Hua, Gu, Xian-Ming, Carpentieri, Bruno, Guo, Jun |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 65M70, 65Y05, 65D25 |
| الوصف: | We propose a Bernoulli-barycentric rational matrix collocation method for two-dimensional evolutionary partial differential equations (PDEs) with variable coefficients that combines Bernoulli polynomials with barycentric rational interpolations in time and space, respectively. The theoretical accuracy $O\left((2\pi)^{-N}+h_x^{d_x-1}+h_y^{d_y-1}\right)$ of our numerical scheme is proven, where $N$ is the number of basis functions in time, $h_x$ and $h_y$ are the grid sizes in the $x$, $y$-directions, respectively, and $0\leq d_x\leq \frac{b-a}{h_x},~0\leq d_y\leq\frac{d-c}{h_y}$. For the efficient solution of the relevant linear system arising from the discretizations, we introduce a class of dimension expanded preconditioners that take the advantage of structural properties of the coefficient matrices, and we present a theoretical analysis of eigenvalue distributions of the preconditioned matrices. The effectiveness of our proposed method and preconditioners are studied for solving some real-world examples represented by the heat conduction equation, the advection-diffusion equation, the wave equation and telegraph equations. Comment: 23 pages, 6 figures, 9 tables (update some contexts) |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.03861 |
| رقم الأكسشن: | edsarx.2402.03861 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |