A simple NSC-RKHS algorithm for solving linear boundary value problems – Error bounds and implementations

摘要

The simple algorithm is in essence a normal spline collocation method introduced by V.K. Gorbunov in 1989. The paper presents a reproducing kernel Hilbert space approach to the method, that gives rise to basic error inequalities. For a natural H2-class of mth order linear problems the approximation of any normal solution v is Cm-1-uniform, i.e. v(a)(t)-vn(a)(t)⩽caΔn2‖v‖Hm+2, for a