سیویلیکا را در شبکه های اجتماعی دنبال نمایید.

Login
PapersConferencesJournals

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

Publish place: Computational Methods for Differential Equations، Vol: 10، Issue: 4
Publish Year: 1401
Type: Journal paper
Language: English
View: 236

This Paper With 14 Page And PDF Format Ready To Download

DOWNLOAD Paper

Export:

Link to this Paper:
https://civilica.com/doc/1595601

Document National Code:

JR_CMDE-10-4_006

Index date: 29 January 2023

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

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.

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

Error analysis , Chebyshev spectral collocation method , Kronecker product , Linear Partial differential equations

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

Mehdi Razavi

Department of Applied Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran.

Mohammad Mehdi Hosseini

Department of Applied Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran.

Abbas Salemi

Department of Applied Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran.

مراجع و منابع این Paper:

لیست زیر مراجع و منابع استفاده شده در این Paper را نمایش می دهد. این مراجع به صورت کاملا ماشینی و بر اساس هوش مصنوعی استخراج شده اند و لذا ممکن است دارای اشکالاتی باشند که به مرور زمان دقت استخراج این محتوا افزایش می یابد. مراجعی که مقالات مربوط به آنها در سیویلیکا نمایه شده و پیدا شده اند، به خود Paper لینک شده اند :
S. Akbarpour, A. Shidfar, and H. Saberinajafi, A Shifted Chebyshev-Tau ...
K. E. Atkinson, The Numerical Solution of Integral Equations of ...
A. G. Atta, W. M. A. Elhameed, and Y. H. ...
I. Celik, Collocation method and residual correction using Chebyshev series, ...
M. Dehghan and M. Lakestani, The use of Chebyshev cardinal ...
W. M. A. Elhameed and Y. H. Youssri, New formulas ...
W. M. A. Elhameed, J. A. Tenreiro Machado, and Y. ...
W. M. A. Elhameed, Y. Youssri, and E. H. Doha, ...
G. Evans, J. Blackledge, and P. Yardley, Analytic Methods for ...
K. Goyal and M. Mehra, Fast diffusion wavelet method for ...
A. S. Hadi, Regression Analysis By Example, WILEY, New Jersey, ...
D. V. Hutton, Fundamentals of finite element analysis, Elizabeth A ...
Y. Jianga and J. Ma, High-order finite element methods for ...
C. Johnson and R. A. Horn, Matrix Analysis, Cambridge Univ. ...
D. Johnson, Chebyshev polynomial in the Tau spectral methods and ...
J. Kevorkian, Partial Differential Equations: Analytical Solution Techniques, Springer, ۱۹۹۹ ...
J. Mason and C. Handscomb, Chebyshev polynomials, CRC Press, ۲۰۱۳ ...
M. Izadi and M. Afshar, Solving the Basset equation via ...
M. Lakestani and M. Dehghan, Numerical solution of fourth-order integro-differential ...
M. Lakestani and M. Dehghan, The use of Chebyshev cardinal ...
A. B. Orovio, V. M. P. Garcia, and F. H. ...
P. Pedersen, New Solutions for Singular Lane-Emden Equations Arising in ...
M. Pourbabaee and A. Saadatmandi, Collocation method based on Chebyshev ...
J. O. Rawlings, S. G. Pantula, and D. K. Dickey, ...
C. K. San, Chebyshev polynomial solutions of second-order linear partial ...
G. Yuksel, O. R. Isik, and M. Sezer, Error analysis ...
Y. H. Youssri, W. M. A. Elhameed, and M. Abdelhakem, ...
Y. H. Youssri and R. M. Hafez, Chebyshev collocation treatment ...
نمایش کامل مراجع