一类特殊边界条件波动方程的有限差分格式

对一类左端为齐次Robin边界,右端为耦合耗散边界的一维波动方程初边值问题构造了一个三层隐式有限差分格式,通过离散能量方法证明了差分格式在无穷范数意义下关于时间和空间均是二阶收敛,并且关于初始条件和右端源项都是无条件稳定的.数值实验验证了理论结果.

A finite difference scheme for the wave equation with a class of special boundary condition

A three-level implicit finite difference scheme is constructed for the initial boundary value problem of one-dimension wave equation with a special boundary condition,which is Robin boundary on the left and the coupling dissipative boundary on the right.The discretized energy method is employed to show that the difference scheme is two-order convergent in the maximum norm with respect to time and space directions and unconditional stable with respect to initial conditions and the right-hand side term.The numerical experiments verify the theoretical results.