Generalized approximations and rapid convergence of solutions of m-point boundary value problems

The upper and lower solutions method and the generalized quasilinearization technique for second order nonlinear m-point boundary value problem of the type-x″=f(t,x,x′),t∈[0,1]δx(0)-γx′(0)=0,x(1)=∑i=1m-2αix(ηi),ηi∈(0,1)is developed. A monotone sequence of solutions of linear problems converging uniformly and quadratically to a solution of the problem is obtained in the C1 norm.