Product integration method for Volterra integral equation with noncompact kernel

摘要

We discuss the Euler method and product trapezoidal method and their convergences for Volterra integral equation with noncompact kernely(t)=∫0tktsy(s)1sds+g(t),t∈[0,T].We first prove that this equation has a unique solution when kernel function k(t) satisfiesα=∫1∞|k(t)|tdt<1.We show that Euler's method and product trapezoidal method are convergent of orders 1 and 2, respectively. Some numerical examples are given to illustrate this theory.