Transcription of Gaussian quadrature - Oklahoma State University–Stillwater
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Gaussian quadrature - Oklahoma State University–Stillwater
Gaussian quadratureTo write a Matlab program using Gaussian quadrature (Gauss-Legendre rule), first you need toknow the weightsciand nodesxi. A typical table of Gauss-Legendre rule looks like the following:n(# of points) Then we can use the formula 1 1f(x)dx n i=1cif(xi),which has the degree of accuracy2n 1. In other words, the above formula is exact for anypolynomialf(x)with degree up to2n you need to integratef(x)on the interval[a, b], simply use a change of variable baf(x)dx= 1 1b a2f((b a)t+ (b+a)2)dt n i=1cib a2f((b a)xi+ (b+a)2)Indeed, we can define ci=cib a2, xi=(b a)xi+ (b+a)2,then the formula can be written as baf(x)dx n i=1 cif( xi).Next, let use look at three Matlab examples of using the Gauss-legendre 1 Compute 1 1excosx dxusing a Gaussian quadrature with 3 points.
Gaussian quadrature To write a Matlab program using Gaussian quadrature (Gauss-Legendre rule), first you need to know the weights c i and nodes x i.A typical table of Gauss-Legendre rule looks like the following:
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