Name
Abstract | ||
|---|---|---|
One of the quadrature rules is the ''Equal coefficients quadrature rules'' represented by@!abw(x)f(x)dx~C"n@?i=1nf(x"i),where C"n is a constant number and w(x) is a weight function on [a,b]. In this work, we show that the precisian degree of above formula can be increased by taking the upper and lower bounds of the integration formula as unknowns. This causes to numerically be extended the monomial space {1,x,...,x^n} to {1,x,...,x^n^+^2}. We use a matrix proof to show that the resulting nonlinear system for the basis f(x)=x^j, j=0,...,n+2 has no analytic solution. Thus, we solve this system numerically to find unknowns x"1,x"2,...,x"n, C"n, a and b. Finally, some examples will be given to show the numerical superiority of the new developed method. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1016/j.amc.2005.01.130 | Applied Mathematics and Computation |
Keywords | Field | DocType |
matrix proof,constant number,nonlinear system,monomial space,analytic solution,integration formula,numerical improvement,equal coefficient,lower bound,quadrature rule,new developed method,numerical integration methods,upper and lower bounds,weight function,numerical integration | Discrete mathematics,Nonlinear system,Weight function,Mathematical analysis,Matrix (mathematics),Upper and lower bounds,Numerical integration,Monomial,Quadrature (mathematics),Numerical analysis,Geometry,Mathematics | Journal |
Volume | Issue | ISSN |
171 | 2 | Applied Mathematics and Computation |
Citations | PageRank | References |
1 | 0.39 | 0 |
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 |