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Razavi, Mehdi, Hosseini, Mohammad Mehdi, Salemi, Abbas. (1401). Error analysis and Kronecker implementation of Chebyshev spectral collocation method for solving linear PDEs. سامانه مدیریت نشریات علمی, 10(4), 914-927. doi: 10.22034/cmde.2021.46776.1966
Mehdi Razavi; Mohammad Mehdi Hosseini; Abbas Salemi. "Error analysis and Kronecker implementation of Chebyshev spectral collocation method for solving linear PDEs". سامانه مدیریت نشریات علمی, 10, 4, 1401, 914-927. doi: 10.22034/cmde.2021.46776.1966
Razavi, Mehdi, Hosseini, Mohammad Mehdi, Salemi, Abbas. (1401). 'Error analysis and Kronecker implementation of Chebyshev spectral collocation method for solving linear PDEs', سامانه مدیریت نشریات علمی, 10(4), pp. 914-927. doi: 10.22034/cmde.2021.46776.1966
Razavi, Mehdi, Hosseini, Mohammad Mehdi, Salemi, Abbas. Error analysis and Kronecker implementation of Chebyshev spectral collocation method for solving linear PDEs. سامانه مدیریت نشریات علمی, 1401; 10(4): 914-927. doi: 10.22034/cmde.2021.46776.1966

Error analysis and Kronecker implementation of Chebyshev spectral collocation method for solving linear PDEs

Computational Methods for Differential Equations
مقاله 6، دوره 10، شماره 4، دی 2022، صفحه 914-927    اصل مقاله (752.18 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 solutions 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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