Hybrid Chebyshev Polynomial Scheme For Solving Elliptic Partial Differential Equations
Document Type
Article
Publication Date
1-15-2020
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
In this paper, we propose hybrid Chebyshev polynomial scheme (HCPS), which couples the Chebyshev polynomial scheme and the method of fundamental solutions into a single matrix system. This hybrid formulation requires solving only one system of equations and opens up the possibilities for solving a large class of partial differential equations. In this paper, we consider various boundary value problems and, in particular, the challenging Cauchy–Navier equation. The solution is approximated by the sum of the particular solution and the homogeneous solution. Chebyshev polynomials are used to approximate a particular solution of the given partial differential equation and the method of fundamental solutions is used to approximate the homogeneous solution. Numerical results show that our proposed approach is efficient, accurate, and stable.
Publication Title
Journal of Computational and Applied Mathematics
Volume
364
Recommended Citation
Khatri Ghimire, B.,
Li, X.,
Chen, C.,
Lamichhane, A.
(2020). Hybrid Chebyshev Polynomial Scheme For Solving Elliptic Partial Differential Equations. Journal of Computational and Applied Mathematics, 364.
Available at: https://aquila.usm.edu/fac_pubs/19114