Solution of Ordinary Differential Equations Using Power Series with Decomposed Coefficients. Part 1. Mathematical Analysis

摘要

The solution functions of systems of ordinary differential equations are represented in form of power series of which the coefficients C/sub n/ are decomposed into three parts C/sub n/ = (A.B.V)/sub n/: A reflects the form of the system, B its strength of coupling and V the initial values. The component A and in most practical cases also the component B remain constant during integration. Recurrence relations for the key-component A are derived for various types of systems. They have the form A/sub n+1/ = f/(A/sub n/). The knowledge of A/sub n/permits a direct, non-recursive computation of the component B and V. This decomposition of the coefficients C/sub n/ permits economical integration of a system (computation of V only instead of C/sub n/ as a whole at each integration step, reduction of coefficients to be computed owing to identities resulting from symmetries of the system), is convenient due to its transparency (intervention on B does not affect A and in most cases also not V), and reveals interesting mathematical information (mathematical significance of A). The formalism is illustrated by examples. 25 refs., 18 tabs. (ERA citation 11:033474)