October 8, 2007
The Accurate Element Method (AEM) can solve in the same way all the problems connected to the Ordinary Differential Equations (ODE) namely the Initial Value Problem (IVP), the Boundary Value Problem (BVP) and the Eigenvalue Problem (EVP). Connected to the IVP problem several academics considered necessary a more elaborate study concerning two essential problems: the stability of the method and its capacities to replace the exact solution of an ODE by several polynomials. This paper is the result of this study. Here we identify two types of problems connected to the integration of the Ordinary Differential Equations: the Target Value Problem (TVP) and the Field Polynomial Solution (FPS). The Accurate Element Method is an implicit method thus generally stable, which makes possible the integration over long intervals leading to accurate solutions with a small number of elements.
The PDF file can be downloaded from here.