Implicit integration methods based on collocation are attractive for a number of reasons, e.g. their ideal (for Gauss-Legendre nodes) or near ideal (Gauss-Radau or Gauss-Lobatto nodes) order and stability properties. However, straightforward application of a collocation formula with M nodes to an initial value problem with dimension d requires the solution of one large Md × Md system of nonlinear equations.
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