On the stability of a weighted finite difference scheme for wave equation with nonlocal boundary conditions ̊

Nonlocal problems is a major research area in many branches of modern physics, biotechnology, chemistry and engineering, which arises when it is impossible to determine the boundary values of unknown function and its derivatives. Increasingly often, there arise problems with nonlocal integral boundary conditions, especially in particle diffusion [1] and heat conduction [2, 3]. Partial differential equations of the hyperbolic type with integral conditions often occur in problems related to fluid mechanics [4] (dynamics and elasticity), linear thermoelasticity [5], vibrations [6] etc. Hyperbolic problems with nonlocal conditions have not been studied so broadly as, say, parabolic or elliptic problems. The paper [7] dealt with the new technique (Adomian Decomposition Method) for solving wave equation with integral boundary conditions. Author consider the one-dimensional wave equation