Fast variants of the NSC–RKHS algorithm for solving linear boundary value problems

摘要

The fast algorithms work in the Sobolev–Hilbert spaces on a finite interval [0,T] and arise from the normal spline collocation method introduced in [4] by Gorbunov and developed within the last 7 years by Chinese mathematicians as a reproducing kernel Hilbert space method. For a natural H4-class of mth order linear problems, Ly=f, two extended variants of the method (applied to an operator Hm+2→H2) yield 4th order uniform approximations of any normal solution v together with its derivatives up to order m-1, i.e. ‖v(b)-vn(b)‖C0⩽cbΔn4‖v‖Hm+4, for b