A comparative study of the Chebyshev collocation method and the finite difference method for solving fourth-order partial differential equations

This study is devoted to a comparison of two numerical methods, the Chebyshev collocation method and the finite difference method (FDM), for solving fourth-order partial differential equations. We provide some examples and compare numerical errors from the two methods. Each problem is transformed to...

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Bibliographic Details
Main Authors: Apornsaengsawang, Somruthai, Neamprem, Khomsan, Chamchod, Farida
Format: Conference Proceeding
Language:English
Subjects:
Chebyshev approximation
Collocation methods
Comparative studies
Discretization
Finite difference method
Initial conditions
Linear algebra
Methods
Numerical methods
Partial differential equations
Viscosity
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Summary:This study is devoted to a comparison of two numerical methods, the Chebyshev collocation method and the finite difference method (FDM), for solving fourth-order partial differential equations. We provide some examples and compare numerical errors from the two methods. Each problem is transformed to linear algebraic equations to solve for unknown Chebyshev coefficients which can be used for approximating solutions at any other points. The problem is then solved by the FDM to obtain results on the discretized domain to approximate solutions at other points. Our results suggest that the accuracy of numerical solutions not only depends on the methods but also discretization strategies. Based on the provided examples, the Chebyshev method can be a powerful tool to solve the fourth-order partial differential equations and their complex forms of boundary and initial conditions and provide better results.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5136496