Factorization Method for the Numerical Solution of Two Point Boundary Value Problems for Linear ODE's (Ordinary Differential Equations)

摘要

The theoretical analysis and computational implementation of factorization-based methods for the numerical solution of linear boundary value problems for ordinary differential equations are presented. The methods are optimal with respect to certain clearly defined criteria. Numerical examples show the effectiveness of a general code based on the factorization method. Direct methods are characterized by the solution of global (linear) algebraic systems for the discrete solution. In this sense multi-shooting may be regarded as a hybrid method between the two classes. A sophisticated recent example of multi-shooting is the BOUNDPAC package. Indirect solution methods are characterized by the association of the boundary value problem with certain auxiliary initial value problems (IVP). The auxiliary IVP's are generally solved uni-directionally (forward), but a subclass of initial value based methods are based on bi-directional (double sweep) strategies.