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 -

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.