Estimation of errors of quadrature formula for singular integrals of Cauchy type with special forms

Details Estimation of errors of quadrature formula for singular integrals of Cauchy type with special forms Estimation of errors of quadrature formula for singular integrals of Cauchy type with special forms

2011-03-05

arxiv.org/abs/1103.1034v1

Mathematics

Numerical Analysis

14 pages, 5 Tables

Scientific paper

In this work, we consider the singular integrals of Cauchy type of the forms $$\ds J(f,x)= \frac{\sqrt{1-x^2}}{\pi}\int_{-1}^1\frac{f(t)}{\sqrt{1-t^2}(t-x)}\,dt, -11$. With the help of linear spline interpolation, we have proved the rate of convergence of the errors of QFs \re{eq3} and \re{eq4} for different classes (i.e. $H^\a([-1,1],K), C^{m,\a}[-1,1], W^r[-1,1]$) of density function $f(t)$. It is shown that approximation by spline possesses more advantages than other kinds of approximation: it requires the minimum smoothness of density function $f(x)$ to get good order of decreasing errors.

Affiliated with

Also associated with

No associations

Rating

Estimation of errors of quadrature formula for singular integrals of Cauchy type with special forms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Estimation of errors of quadrature formula for singular integrals of Cauchy type with special forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Estimation of errors of quadrature formula for singular integrals of Cauchy type with special forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-8766