具有非局部边值条件的波动方程的加权隐式差分格式

许多物理现象是由具有非局部条件的双曲型方程描述的.具有非局部条件的双曲型方程的数值解法是一个重要研究领域,在现代科学与技术科学有广泛应用.本文讨论了一类具有非局部边值条件的双曲型方程的数值解.通过引入新的未知函数将一类具有非局部边值条件的波动方程定解问题变为Dirichlet和Neumann边值问题,作者给出了该问题的加权隐式差分格式,证明了该差分格式的唯一可解性,利用Fourier方法给出了上述差分格式的稳定性条件.给出的数值例子用以说明差分格式稳定性和收敛性.

A weighted implicit difference scheme for the wave equation with nonlocal boundary condition

Many physical phenomena are modeled by the hyperbolic equations with nonlocal boundary value condition. Numerical solution of hyperbolic partial differential equation with an integral condition is a major research area with widespread applications in modern science and technology. Numerical solution of a hyperbolic boundary value problem with nonlocal condition is discussed in this paper. This hyperbolic boundary value problem with nonlocal condition is changed into a hyperbolic boundary value problem with Dirichlet and Neumann boundary value condition by means of a new unknown function. A weighted implicit difference scheme for the aforesaid hyperbolic boundary value problem is given. The existence and uniqueness of the solution of the weighted implicit difference scheme is proven. The stability condition of the weighted implicit difference scheme is obtained. Two numerical examples showing stability and convergence are given.