一类黏性波动方程的局部一维差分格式

A locally one-dimensional finite difference scheme for a class of viscous wave equations

针对二维黏性波动方程,利用Crank-Nicolson格式建立了在时间和空间方向具有二阶精度的差分格式,通过添加扰动项进行算子分解,得到了一类局部一维差分格式,证明了该格式按离散L2模具有二阶收敛精度.具体算例验证了算法的有效性和精确性.

By using Crank-Nicolson method a finite difference scheme with two-order accuracy in space and time is proposed for the viscous wave equations of two-dimension. After perturbing a locally one-dimensional finite difference scheme is obtained by decomposing the difference scheme. The scheme is confirmed two-order convergence accuracy in discrete L2 norm. A numerical example proves its accuracy and validity.