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)≤ ~(ca)Δn2vHm+ ~2, for a