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

Abstract

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.