【摘要】 <正> 1.引言 用三次样条求解粘性流体力学问题的数值方法已有了相当的发展。为了探讨用该方法求解无粘流动问题的可能性,本文尝试把差分方法中一些典型的计算格式扩展到样条方法,提出了样条Lax-Wendroff格式和样条跳蛙格式。以一维模型方程为例,按照Warming等的方法导出了它们的修正方程,分析了格式的稳定条件及数值弥散和耗散效应。然后扩展到对一般非线性双曲方程求解的研究。最后,讨论了某些数值解例。更多还原

【Abstract】 For exploring the possibility to solve the equation of inviscous flow using cubic spline?in this paper,Spline-Lax-Wendroff scheme and Spline-Leap-Frog scheme to one-dimensional hyperbolic equation are introduced.Their modified equations are derived.The stability of the schemes as well as the numerical dispertive and dissipative effects are analyzed by studying the modified partial differential equation.The computation results indicate that good results can be obtained by means of the spline schemes.更多还原