TY - JOUR
T1 - Efficient Algorithms for Approximating Particular Solutions of Elliptic Equations Using Chebyshev Polynomials
AU - A. Karageorghis & I. Kyza
JO - Communications in Computational Physics
VL - 3
SP - 501
EP - 521
PY - 2007
DA - 2007/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7915.html
KW - Chebyshev polynomials, Poisson equation, biharmonic equation, method of particular solutions.
AB - <p style="text-align: justify;">In this paper, we propose efficient algorithms for approximating particular solutions of second and fourth order elliptic equations. The approximation of the particular solution by a truncated series of Chebyshev polynomials and the satisfaction of the differential equation lead to upper triangular block systems, each block being an upper triangular system. These systems can be solved efficiently by standard techniques. Several numerical examples are presented for each case.</p>