波动问题的高精度重心有理插值配点法

提出一种数值求解波动问题的高精度重心有理插值配点法。对于给定的时间和空间上的计算节点，采用重心有理插值近似未知函数，建立未知函数关于时间和空间变量导数的微分矩阵。将未知函数的重心有理插值近似函数代入波动问题的控制方程，得到波动问题方程和定解条件的离散代数方程组。利用微分矩阵的记号，将离散后的代数方程组写成简洁的矩阵形式。通过置换法施加边界条件和初始条件，求解代数方程组，得到波动问题在计算节点处的位移值。数值算例表明，重心有理插值配点法具有计算公式简单、计算节点适应性好、程序实施方便和计算精度高的优点。

High-precison barycentric rational interpolation collocation method of wave problems

We construct the differentiation matrices of an unknown function regarding temporal and spatial variables for the given computational nodes in temporal and spatial fields with the approaximation of barycentric rational interpolation to the function.We initially acquire discrete algebraic equations of a wave equation and its definite conditions by inserting barycentric rational interpolation of an unknown function into the governing equation of the wave equation.We then denote the discrete algebraic equations as a concise matrix with the notation of differentiation matrices.We eventually obtain the displacements of the wave equation on the nodes by replacement method and applying boundary and initial conditions.Numerical examples demonstrate that the approach has such advantages as simple computation,easy programming and high precision.