梁振动方程一类稳定的紧致差分格式

A Stable Compact Finite Difference Scheme for the Beam Equation

针对四阶梁振动方程运用有限差分方法,构造一类无条件稳定的紧致差分格式。利用Fourier级数法验证差分格式的收敛性,并运用Lax等价性定理证明了格式的稳定性,最后通过两组数值实验证明格式的有效性和实用性,并最终将格式的收敛阶精度由之前的o(τ+h2)提高至o(τ+h4)便于科学和工程计算中的更好应用。

In this paper,an unconditional stable compact finite difference scheme is proposed for the beam equation with fourth- order by using the finite difference method. The stability and convergence of the difference scheme are demonstrated by Fourier method and Lax equivalence theorem. Two numerical experiments have been carried out to confirm the effectiveness and the practicability of the scheme and the convergence order is improved at last. The result will promote the better application in science and engineering calculation.