The numerical experiments proved that the improved algorithm has the characteristics of easily to program and precision higher . based on it , detailed computational procedure package and curve storehouse of arbitrary kinds of mathieu function has also been obtained 數(shù)值實(shí)驗(yàn)證明,這種改進(jìn)后的算法具有易編程,精確度更高的特點(diǎn)。并在此基礎(chǔ)上給出了完整的計(jì)算程序包,建立了目前最為完整的mathieu函數(shù)曲線庫(kù)。
Mathieu function is the base of field theory analysis in elliptical cylinder coordinate system . so , firstly , detail investigation has been given about the problem of numerical analysis of matheiu functions , based on the predecessor ' s contribution , an improved faster algorithm of numerical analysis and confirmation algorithm of matheiu functions has been presented Mathieu函數(shù)是橢圓柱坐標(biāo)系統(tǒng)下場(chǎng)論分析的基礎(chǔ),因此本文首先對(duì)mathieu函數(shù)的數(shù)值計(jì)算問(wèn)題進(jìn)行了詳細(xì)研究,并在前人基礎(chǔ)上完善并進(jìn)一步改進(jìn)了目前被認(rèn)為較為可行的數(shù)值算法,并提出了驗(yàn)證算法。
The major achievements are listed as the followings : mathieu functions remain difficult to employ , mainly because of the impossibility of analytically representing them in a simple and handy way . the methods for the computation of all mathieu functions of integer orders for large range of the order n and the parameter q were presented here . the calculations were made by programs using matlab to compute the mathieu functions 本論文的主要工作:由于在使用馬丟函數(shù)時(shí)存在一些困難,主要是因?yàn)椴荒芎?jiǎn)單方便地對(duì)其進(jìn)行解析表示,我們給出整數(shù)階各類馬丟函數(shù)的詳細(xì)計(jì)算方法,該方法適合較大范圍的階數(shù)n和參數(shù)q值,實(shí)際計(jì)算中采用了matlab軟件進(jìn)行編程實(shí)現(xiàn),并給出了各類馬丟函數(shù)在自變量和q值兩個(gè)參數(shù)變化下的三維可視化圖形。