The MAPS Based On Trigonometric Basis Functions For Solving Elliptic Partial Differential Equations With Variable Coefficients and Cauchy-Navier Equations
Document Type
Article
Publication Date
5-1-2019
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
In this paper, we extended the method of approximate particular solutions (MAPS) using trigonometric basis functions to solve two-dimensional elliptic partial differential equations (PDEs) with variable-coefficients and the Cauchy–Navier equations. The new approach is based on the closed-form particular solutions for second-order differential operators with constant coefficients. For the Cauchy–Navier equations, a reformulation of the equations is required so that the particular solutions for the new differential operators are available. Five numerical examples are provided to demonstrate the effectiveness of the proposed method.
Publication Title
Mathematics and Computers in Simulation
Volume
159
First Page
119
Last Page
135
Recommended Citation
Wang, D.,
Chen, C.,
Fan, C.,
Li, M.
(2019). The MAPS Based On Trigonometric Basis Functions For Solving Elliptic Partial Differential Equations With Variable Coefficients and Cauchy-Navier Equations. Mathematics and Computers in Simulation, 159, 119-135.
Available at: https://aquila.usm.edu/fac_pubs/15995