一维粘性波动方程的三层紧致差分格式

A Three Level Compact Difference Scheme for Solving a One-dimensional Viscous Wave Equation

对一维粘性波动方程,构造一个三层紧致差分格式,并利用能量法进行误差分析,证明差分格式在最大范数意义下有O(τ~2+h^4)的收敛阶。利用Richardson外推法,得到O(τ~4+h^4)的外推解。最后,给出数值算例,验证了该差分格式的收敛阶和有效性。

A three level compact finite difference scheme for solving a one-dimensional viscous wave equation is derived. Using the energy method for error analysis,it is proved that the difference solution converges to exact solution with a convergence order of O( τ~2+ h^4) in the maximum norm. Moreover,the Richardson extrapolation method is utilized to make the final solution fourth-order accurate in both time and space. Finally,a numerical example is provided to verify the convergence order and validity of the difference scheme.