求解二阶波动方程的三次样条差分方法

有限差分法在求解二阶波动方程初边值问题过程中通常受到精度和稳定性的限制.本文对二阶波动方程的时间、空间项分别采用三次样条公式进行离散,推导出精度分别为O(τ2+h2),0(τ2+h4),O(τ4+h2)和O(τ4+h4)的四种三层隐式差分格式,以及与之相匹配的第一个时间步的同阶离散格式,并采用Fourier方法分析了格...

Cubic Splines Difference Method for Solving the Second Order Wave Equation

In solving initial boundary value problem of the second order wave equation,the classical finite difference method is generally restricted by its stability and precision.In this paper,four classes of three-level implicit schemes are proposed for solving the one-dimensional wave equation by using cubic-spline function.Those methods are of order O(τ2+h2),O(τ2+h4),O(τ4+h2) and O(τ4+h4)respectively.Stability conditions are obtained by Fourier analysis method.It is shown by numerical examples that the two schemes presented in this paper are much better than the precise time-integration method,the classical C-N method and the high accuracy compact schemes,and they have high accuracy even for a long time calculation.In addition,the current schemes include the high accuracy compact scheme as a special case.