色散方程ut=auxxx的一类具高稳定性的三层显式格式
A Class of Three-Level Explicit Schemes with Higher Stability Properties for a Dispersive Equation ut=auxxx
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摘要: 本文对色散方程u1=auxxx提出一类三层显式格式,它的稳定性条件为|r|=|a|△t/(△x)3≤2.382484,比[1,2]中的|r|≤0.3849和[3]中的|r|≤0.701659以及[4]中的|r|≤1.1851有较大改进.Abstract: In this paper, a class of three level explicit schemes for a dispersive equation ut =auxxx with stability condition |r|=|a|△t/(△x)3≤2.382484, are considered. The stability condition for this class of schemes is much better than |r|≤0.3849 in [1], [2] and |r|≤0.701658 in [3], and |r|≤l.1851 in [4].
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[1] Zabusky,N.J.and M.Kruskal,Interaction of "Solutions" in a collisionless plasma and the recurrence of initial states,Phy.Rev.Letters,15(1965),240-243. [2] 秦孟兆,色散方程ut=auxxx的差分格式,计算数学,6,1 (1984).1-13. [3] 黎益、李北杰,关于色散方程ut=auxxx的两个显式差分格式,计算数学,8,3 (1986),275-280. [4] 邬华漠,一类具高稳定性的三层显式格式H3,计算数学,8,3 (1986),329-331. [5] Miller,J.J.H.,On the location of zeros of certain classes of polynomials with application to numerical analysis,J.Inst.Math.Appl.8(1971),397-406. [6] Richtmyer,R.D.and K.W.Morton,Difference Method for Initial Value Problems,2nd edi.,Wiley,New York(1976). -
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