| [ KAIST ] in KIDS 글 쓴 이(By): oparrow (열린화살) 날 짜 (Date): 2000년 8월 30일 수요일 오후 01시 24분 32초 제 목(Title): Re: 도데체 그네의 원리가 뭡니까? I introduce a method to improve the accuracy of the singular integrals. Let us consider the integral I=PV\int_{p-\Delta}^{p+\Delta} \frac{f(\lambda)}{g(\lambda)}d{\lambda} where the integrand has a simple pole at \lambda=p, i.e.; f(p)\neq0; g(p)=0; g'(p)\neq=0 "Folding around the pole" Foding the interval around its middle, reducing it to [p-\Delta,p]; in mathematical terms I=\int_{p-\Delta}^{p}F(\lambda}d\lambda F(\lambda)=f(\lamda)/g(\lambda)+f(2p-\lambda)/g(2p-\lambda) where the new integrand is no longer singular at \lambda=p, since it can be shown that F(p)=[2f'(p)g'(p)-f(p)g''(p)]/[g'(p)]^2 and F'(p)=0 The other method is the extraction of singularity. Numerically, these two methods are strictly equivalent, if the location of the pole is known exactly. |