TY - JOUR
T1 - A New Collocation Method for Solving Certain Hadamard Finite-Part Integral Equation
AU - Feng , Hui
AU - Gao , Yan
AU - Ju , Lili
AU - Zhang , Xiaoping
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 240
EP - 254
PY - 2018
DA - 2018/10
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/12802.html
KW - Hadamard finite-part integral equation, quadrature rule, collocation method, error analysis.
AB - <p style="text-align: justify;">In this paper, we study a new nodal-type trapezoidal rule for approximating Hadamard
finite-part integrals, and its application to numerical solution of certain finite-part integral equation.
We start with a nodal-type trapezoidal rule discussed in [21], and then establish its error
expansion analysis, from which a new nodal-type trapezoidal rule with higher order accuracy is
proposed and corresponding error analysis is also obtained. Based on the proposed rule, a new
collocation scheme is then constructed to solve certain finite-part integral equation, with the optimal
error estimate being rigorously derived. Some numerical experiments are also performed to
verify the theoretical results.</p>