Adaptivity and Computational Complexity in the Numerical Solution of ODEs
In this paper we analyze the problem of adaptivity for numerical methods for solving ODEs, both IVPs and BVPs, with a view to generating optimal grids for local error control. The grids are generated by introducing an auxiliary independent variable au and finding a grid deformation map, t=Theta(au), that maps an equidistant grid au_j to a non-equidistant grid in the original independent variable,
