Piecewise Analytical Perturbation Series Methods for Solving Linear Ordinary Differential Equations. 1. General Schemes for Algorithm Implementation

摘要

The piecewise analytical perturbation series (PAPS) approach to the solution of linear ordinary differential equations is shown to provide both PAPS algorithms and equations for the accumulated discretization errors, each of which involving the same set of propagators, a property which is very important for the implementation of PAPS codes with global control over the discretization error. Finite, simple and flexible PAPS algorithms can be derived provided the coefficients of the given differential equation are approximated by trucated piecewise Legendre series. Theoretical realization of such algorithms are outlined and their orders of accuracy are established. (Atomindex citation 16:078608)