Name
Title | ||
|---|---|---|
The first kind Chebyshev-Newton-Cotes quadrature rules (closed type) and its numerical improvement |
Abstract | ||
|---|---|---|
One of the less-known integration methods is the weighted Newton-Cotes of closed type quadrature rule, which is denoted by:@!a=x"0b=x"n=x"0+nhf(x)w(x)dx~@?k=0nw"kf(x"0+kh),where w(x) is a positive function and h=b-an is a positive value. There are various cases for the weight function w(x) that one can use. Because of special importance of the weight function of Gauss-Chebyshev quadrature rules, i.e. w(x)=11-x^2 in numerical analysis, we consider this function as the main weight. Hence, in this paper, we face with the following formula in fact:@!-1+1f(x)1-x^2dx~@?k=0nw"kf-1+2kn.It is known that the precision degree of above formula is n+1 for even n's and is n for odd n's, however, if we consider its bounds as two additional variables we reach a nonlinear system that numerically improves the precision degree of above formula up to degree n+2. In this way, we give several examples which show the numerical superiority of our approach. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1016/j.amc.2004.09.048 | Applied Mathematics and Computation |
Keywords | Field | DocType |
gauss-chebyshev quadrature rule,following formula,precision degree,weight function w,weight function,odd n,numerical improvement,degree n,main weight,positive function,closed type quadrature rule,numerical analysis,nonlinear system,quadrature rule | Weight function,Mathematical analysis,Numerical integration,Newton–Cotes formulas,Quadrature (mathematics),Numerical analysis,Gaussian quadrature,Gaussian function,Mathematics,Newton's method | Journal |
Volume | Issue | ISSN |
168 | 1 | Applied Mathematics and Computation |
Citations | PageRank | References |
5 | 0.80 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. R. Eslahchi | 1 | 88 | 13.65 |
| Mehdi Dehghan | 2 | 3022 | 324.48 |
| M. MasjedJamei | 3 | 63 | 18.98 |