Could somebody please explain wht the term 'single point quadrature' means. Is it some scheme for intergration?
Thanks Nic
Quadrature is in general a method for evaluating intergrals numerically which otherwise cannot be solved using elementary forms. In this case, single point quadrature is likely referring to a method whereby in each subinterval of the total interval over which the integral is defined, only one point of the integrand will be evaluated. But this is for each subinterval. Summing the subintervals (where for each subinterval we're computing its area numerically, i.e., the one point where the function gets evaluated (the height) times the width of the subinterval (the base)), we get an approximation of the total area, i.e., the value of the integral. The above is referring to the one dimensional case.
In this case, it appears one point quadrature may be referring to the midpoint rule.
"Quadrature", in general, refers to any numerical integration, though it is sometimes used specifically to refer to Simpson's rule which approximates the integrand by a piecwise quadratic function.
I was not familiar with "one point quadrature" so I googled it and got a number of hits. The first was to your question! The others were to papers and books on numerical solution of partial differential equations. I get the impression the "one point quadrature" refers to doing a numerical integration with respect to one variable, say time, at each specific point in a grid (interpreting the other variables as space coordinates).
actually, if you look here, Numerical integration - Wikipedia, the free encyclopedia
you will note examples (about one rotation of your mouse wheel down)where only one point is used to approximate an intergral over its bounds. perhaps that's what your question is referring to. i was talking about this but applied to each subinterval of the interval, not to the entire interval.