Gaussian quadrature rules using function derivatives

For finite positive Borel measures supported on the real line we consider a new type of quadrature rule with maximal algebraic degree of exactness that involves function derivatives. We prove the existence of such quadrature rules and describe their basic properties. We also give an application of these quadrature rules to the solution of a Cauchy problem without solving it directly. Numerical examples are included as well.

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Original source : http://imajna.oxfordjournals.org/cgi/content/short...