On Algebraic Preprocessing of Floating-Point DAEs for Numerical Model Simulation

This paper investigates the cancellation errors which may occur in algebraic preprocessing with floating-point numbers, of numerical model simulation. We consider two operations, the substitution of a polynomial for terms of other polynomials and solving system of parametric linear equations. For the first operation, we clarify that the "gsystematic term-cancellation" may cause large errors and propose a simple method to avoid large errors. The idea is to introduce system parameters of value 1 to avoid mixing of terms which may cancel one another. For the second operation, we propose a combined method of numerical Gauss-Jordan elimination with pivoting and the symbolic minor expansion of the parametric determinants. There may occur the case that the pivoting is unsatisfactory or restricted severely, hence we propose two error-avoiding methods, they can be used together with pivoting. We convince ourselves of the effectiveness of proposed methods by experiments.