二阶双曲型方程双参数差分格式

Second-order hyperbolic equation difference schemes with two parameters

对一维二阶双曲型方程2u/t2=C2 2u/x2,构造了一个双参数三层差分格式,并讨论了它的稳定性与收敛性.当参数适当选取时,其局部截断误差阶可达O(τ4+h4)或O(τ6+h6),且其稳定性条件为r=Cτ/h≤1或r=1.

Abstract： Three -level difference schemes with two parameters are presented for solving the equation of one - dimensional and second - order hyperbolic typeδ^2u/δt^2=C^2δ^2u/δx^2and their stability and convergence property are discussed. The order of the local discretization are O（τ^4＋h^4） or O（τ^6＋h^6） with choice apropos parameters, and the stability conditions arer=Cτ-/h≤1 or r = 1.