- 期刊
RAPID CONVERGENCE OF APPROXIMATE SOLUTIONS FOR FIRST ORDER NONLINEAR BOUNDARY VALUE PROBLEMS
摘要
In this paper we study the convergence of the approximate solutions for the following first order problem u'(t) = f(t,u(t));t ∈ [0,T], au(0)-bu(t_0) = c,a,b ＞ 0, a + b ＞ 0, t_0 (0,T]. Here f: I x R →R is such that □ exists and is a continuous function for some k ≥ 1. Under some additional conditions on □, we prove that it is possible to construct two sequences of approximate solutions converging to a solution with rate of convergence of order k.