A Uniqueness Theorem for a Boundary Value Problem

Abstract

In this paper it is proved that the two-point boundary value problem, namely $({d^{(4)}}/d{x^4} + f)y = g,y(0) - {A_1} = y(1) - {A_2} = y''(0) - {B_1} = y''(1) - {B_2} = 0$, has a unique solution provided ${\inf _x}f(x) = - \eta > - {\pi ^4}$. The given boundary value problem is discretized by a finite difference scheme. This numerical approximation is proved to be a second order convergent process by establishing an error bound using the ${L_2}$-norm of a vector.