具Robin型阻尼边界二维波动方程的隐式有限差分格式

Finite Difference Scheme for Two-Dimensional Wave Equation with Damped Robin Boundary

考虑左边界为零,右边界含Robin型阻尼项的二维波动方程,利用Taylor级数公式展开可得三层离散的隐式差分格式.将离散乘子法和Gronwall不等式用于证明该隐式格式在无穷维范数意义下数值解的存在性,收敛性以及稳定性.另外,可知该格式在时间和空间方向都为二阶精度.用一个数值算例验证了所建格式的理论结果.

The two-dimensional wave equation with the left boundary being zero and the right boundary containing the Robin-type damping term is considered. The three-layer discrete implicit difference scheme is obtained by using the Taylor formula. The discrete multiplier method and Gronwall inequality are used to prove the existence, convergence and stability of numerical solutions about the implicit format in the sense of infinite dimensional norm. The format maintains second-order precision in both time and space directions. A numerical example is used to verify the theoretical resuhs of the proposed format.