Projection methods and approximations for ordinary differential equations

A formulation of a differential equation as projection and fixed point problem allows approximations using general piecewise functions. We prove existence and uniqueness of the approximate solution, convergence in the L₂ norm and nodal superconvergence. These results generalize those obtained earlier by Hulme for continuous piecewise polynomials and by Del four-Dubeau for discontinuous piecewise polynomials. A duality relationship for the two types of approximations is also given. This research has been supported in part by the Natural Sciences and Engineering Research Council of Canada (Grant OGPLN-336) and by the “Ministère de l’Education du Québec” (FCAR Grant-ER-0725).