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单调二次样条插值及其在状态方程计算中的应用

MONOTONE QUADRATIC SPLINE INTERPOLTIONAND ITS APPLICATIONS TO THE CONMPU-TATION OF STATE EQUATIONS

    摘要
  • 摘要: 本文证明了如下结果:设a,b,ya,yb,ya',yb',均为实数,满足aab;ya'≥0,yb'≥0;则当ya'+yb'≤4(yb-ya)/(b-a)时,满足s(a)=ya,s(b)=yb,S'(a)=ya',S'(b)=yb'的以a,(a+c)/(2),b为插值节点的单调增加二次样条函数S(x)εC'a,b存在且唯一,而且当ya'+yb'>4((yb-ya)/(b-a))时,满足上述要求的二次插值样条函数不存在。根据这个结果讨论了多节点单调二次插值样条函数的存在性,并且给出了在不同区域间状态方程的能量与压强曲面光滑衔接的一个计算方法。

     

    Abstract: This note proues the following result. Let a, b, ya, yb, ya', yb'be real numbers satisfying aab;ya'≥0,yb'≥0;ya'+yb'≤4((yb-ya/(b-a))) then the mo-notone increasing quadratic spline S(x)∈C1a,bwith knots at a,(a+b)/(2), b existsand is unique, and if ya'+yb'4((yb-ya)/(b-a)), such quadratic interpolating spline do-es not exist.According to this result the paper studies the existence of monotone cuadratic interpolating splines with more knots, and gives a computational method of smoothly Linking up the energy and pressure surfaces between different regions of state equations.

     

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