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Error analysis and Kronecker implementation of Chebyshev spectral collocation method for solving linear PDEs | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 22 آذر 1400 اصل مقاله (471.02 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2021.46776.1966 | ||
| نویسندگان | ||
Mehdi Razavi؛ Mohammad Mehdi Hosseini؛ Abbas Salemi  
| ||
| Department of Applied Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran. | ||
| چکیده | ||
| Numerical methods have essential role to approximate the so- lutions of Partial Differential Equations (PDEs). Spectral method is one of the best numerical methods of exponential order with high convergence rate to solve PDEs. In recent decades the Chebyshev Spectral Collocation (CSC) method has been used to approximate solutions of linear PDEs. In this paper, by using linear algebra operators, we implement Kronecker Chebyshev Spectral Collocation (KCSC) method for n-order linear PDEs. By statistical tools, we obtain that the Run times of KCSC method has polynomial growth, but the Run times of CSC method has exponential growth. Moreover, error upper bounds of KCSC and CSC methods are compared. | ||
| کلیدواژه‌ها | ||
| Error analysis؛ Chebyshev spectral collocation method؛ Kronecker product؛ linear Partial differential equations | ||
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آمار تعداد مشاهده مقاله: 45 تعداد دریافت فایل اصل مقاله: 91 |
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