TY - GEN
T1 - A comparative study of the Chebyshev collocation method and the finite difference method for solving fourth-order partial differential equations
AU - Apornsaengsawang, Somruthai
AU - Neamprem, Khomsan
AU - Chamchod, Farida
N1 - Publisher Copyright:
© 2019 Author(s).
PY - 2019/12/4
Y1 - 2019/12/4
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/85076765584
U2 - 10.1063/1.5136496
DO - 10.1063/1.5136496
M3 - Conference contribution
AN - SCOPUS:85076765584
T3 - AIP Conference Proceedings
BT - Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018
A2 - Yatim, Yazariah Mohd
A2 - Ahmad, Syakila
A2 - Ismail, Mohd Tahir
A2 - Ali, Majid Khan Majahar
A2 - Rahman, Rosmanjawati Abdul
A2 - Sulaiman, Hajar
A2 - Ramli, Norshafira
A2 - Ahmad, Noor Atinah
A2 - Abdullah, Farah Aini
PB - American Institute of Physics Inc.
T2 - 1st International Conference on Mathematical Sciences and Technology 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation, MathTech 2018
Y2 - 10 December 2018 through 12 December 2018
ER -