Bessel-Neumann混合型方程特征根系的求解方法
Extraction of Characteristic Roots on BesseLl-Neumann’s Mixed Equations
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摘要: 本文讨论了Bessel-Neumann混合型方程特征根系{λt}(λ0λ1λ2…)的求解法问题.给出了计算特征根系的表达式和最小根的取值方法.这种计算方法的优点是不用多位的Bessel函数表,也不需要计算机就能快速地计算出特征根系{λt}并具有较高的计算精度.Abstract: This paper discusses the problem of the extraction of characteristic roots {λt}(λ0<λ1<λ2…) on Bessel-Neumann's mixed equations. It gives the expressions and the evaluation of the minimum root. The advantage of the method has no use for the table of the multi-figure number Bessel function and it does not need computer but can calculate all the characteristic roots {λt}. The precision of these roots is still high.
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[1] Yih,C.S.(易家训),Fluid Mechanics,McGraw-Hill,New York(1969). [2] Lin,C.C.(林家翘),The Theory of Hydrodynamic Stability,Cambridge University Press,Cambridge(1955). [3] Bogert,B.P.,Some roots of an equation involving Bessel functions,J.Math.Phys.,30(1951),102-105. -
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