浅水方程初边值问题几种新的差分格式及其数值试验

本文提出几种有限差分法求解绝对坐标系中浅水方程的新方法;对五个对角线矩阵也提出了效率高而且简单的两级迭代计算的有效方法.这种迭代法可以用来处理浅水方法的多格计算.最后我们研究了初始边界值问题.通过数值试验证明,线性正弦波会逐步变为非线性的圆锥型波.

Several New Types of Finite-Difference Schemes for Shallow-Water Equation with Initial-Boundary Value and Their Numerical Experiment

This paper proposed several new types of finite-difference methods for the shallow water equation in absolute coordinate system and put forward an effective two-step predictor-corrector method, a compact and iterative algorithm for five diagonal matrix. Then the iterative method was used for a multi-grid procedure for shallow water equation. At last, an initial-boundary value problem was considered, and the numerical results show that the linear sinusoidal wave would successively evolve into conoidal wave.