Accuracy of Implicit Runge-Kutta Methods

As we consider in this book only implicit Runge-Kutta methods which are based on collocation methods, accuracy results of these methods are very much related to the accuracy properties of interpolation polynomials. 

We cite from [HNW87] the following central result 

that the order is defined via the global error in the discretization points tn-If we evaluate the collocation polynomial between these points and compare the result with the exact solution of the differential equation one usually gets a lower order (cf. Sec. 4.5). This phenomenon is called superconvergence of collocation methods. 

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