Multipoint Approach to the Two-Point Boundary Value Problem

摘要

The paper treats nonlinear, two-point boundary-value problems of the form dx/dt - phi (x,t)=0, in which the Jacobian matrix (phi sub x)(x,t) is characterized by large positive eigenvalues. The resulting numerical difficulties are reduced by treating the two-point boundary-value as a multipoint boundary-value problem. A totally finite-difference approach is employed, thus bypassing the often troublesome integration of the nonlinear equations, which characterizes shooting methods. (Author)