Name
Abstract | ||
|---|---|---|
A weighted quadrature rule of interpolatory type is represented as @!"a^bf(x)w(x)dx=@?k=0nw"kf(x"k)+R"n"+"1[f], where w(x) is a weight function, {x"k}"k"="0^n are integration nodes, {w"k}"k"="0^n are the corresponding weight coefficients, and R"n"+"1[f] denotes the error term. During the past decades, various kinds of formulae of the above type have been developed. In this paper, we introduce a type of interpolatory quadrature, whose nodes are geometrically distributed as x"k=aq^k, k=0,1,...,n, and obtain the explicit expressions of the coefficients {w"k}"k"="0^n using the q-binomial theorem. We give an error analysis for the introduced formula and finally we illustrate its application with a few numerical examples. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.mcm.2010.11.076 | Mathematical and Computer Modelling |
Keywords | Field | DocType |
node polynomials,integration node,newton interpolation,q-binomial theorem,error analysis,geometric node,explicit form,error term,weighted quadrature rule,geometric nodes,explicit expression,interpolatory quadrature,weighted quadrature rules,interpolatory type,weight function,numerical example,corresponding weight coefficient,geometric distribution,quadrature rule | Discrete mathematics,Mathematical optimization,Weight function,Expression (mathematics),Mathematical analysis,Generic property,Quadrature (mathematics),Function composition,Gaussian quadrature,Mathematics | Journal |
Volume | Issue | ISSN |
53 | 5-6 | Mathematical and Computer Modelling |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mohammad Masjed-Jamei | 1 | 15 | 8.03 |
| Gradimir V. Milovanović | 2 | 45 | 11.62 |
| M. A. Jafari | 3 | 0 | 0.34 |