Interval Analysis and Two-Point Boundary Value Problems
Fernanda Almeida da Silva de Sá Oliveira · SIAM Journal on Numerical Analysis · 1974
Two error bounding methods for two-point boundary value problems are presented. Using the simple factorization method and interval analysis we find the numerical solution of two-point boundary value problems of linear type with complete error bounds. The numerical solutionis given as an interval which always contains the exact solution. In the second part of this paper we present a corrector method applicable to linear and nonlinear problems—the $(2 \times 2)$ interval discretization method—which is a slight modification of Hansen’s method [3] and enables us to improve previously given results.