Superconvergence of the composite Simpson’s rule for a certain finite-part integral and its applications

The superconvergence of the composite mi

The superconvergence of the composite midpoint rule for the finite-part integral

✍ Jiming Wu; Zihuan Dai; Xiaoping Zhang 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 748 KB

The composite midpoint rule is probably the simplest one among the Newton-Cotes rules for Riemann integral. However, this rule is divergent in general for Hadamard finite-part integral. In this paper, we turn this rule to a useful one and, apply it to evaluate Hadamard finite-part integral as well a