January 28, 2009
It is usually considered that an ordinary differential equation (ODE) can have on the whole integration domain either an analytic solution φ(x) (which replaced in the ODE leads to an identity) or a numeric solution (represented by a string of numerical values whose accuracy is more difficult to quantify). The integration of an ODE by the Accurate Element Method leads to Piecewise Polynomial Solutions represented by a small number of polynomials, each one valid on a single sub-domain (element); they can be considered as quasi-analytic solutions. A quasianalytic solution is suitable for verification by replacing it in the ODE that does not lead to identities but to a quantifiable residual. Based on the value of the residual one can decide either to accept the solution or to compute it once again with slightly modified parameters until an imposed allowable precision is reached. This paper presents a strategy valid for both cases.
The PDF file can be downloaded from here.