The Numerical Solution of Boundary Value Problems for Second Order Functional Differential Equations by Finite Differences.

摘要

The boundary value problem x double prime (t) = g(t,x(t)) + (kappa x)(t), 0 < t < 1, x(0) = x(1) = 0,is considered. Here g : (R sup 2)(arrow)(R sup 1) and kappa :rho(0,1) (arrow) rho(0,1). The solution x is approximated using finite differences. For a large class of problems it is proved that the approximate solutions exist and converge to x. The method is illustrated by the numerical example. (Author)