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

Document Type : Research Paper

Authors

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

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.

Keywords

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### History

• Receive Date: 02 July 2021
• Revise Date: 07 December 2021
• Accept Date: 12 December 2021
• First Publish Date: 13 December 2021