TY - JOUR
T1 - Implicity Linear Collocation Method and Iterated Implicity Linear Collocation Method for the Numerical Solution of Hammerstein Fredholm Integral Equations on 2D Irregular Domains
AU - Laeli Dastjerdi , H.
AU - Ahmadabadi , M. Nili
JO - Journal of Computational Mathematics
VL - 4
SP - 624
EP - 637
PY - 2020
DA - 2020/04
SN - 38
DO - http://doi.org/10.4208/jcm.1903-m2017-0206
UR - https://global-sci.org/intro/article_detail/jcm/16466.html
KW - Two dimensional equations, Irregular domain, Fredholm integral equations, Meshless method, Numerical treatment.
AB - <p style="text-align: justify;">In this work, we adapt and compare implicity linear collocation method and iterated
implicity linear collocation method for solving nonlinear two dimensional Fredholm integral
equations of Hammerstein type using IMQ-RBFs on a non-rectangular domain. IMQs
show to be the most promising RBFs for this kind of equations. The proposed methods
are mesh-free and they are independent of the geometry of domain. Convergence analysis
of the proposed methods together with some benchmark examples is provided which
support their reliability and numerical stability.</p>