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)值實驗證明,這種改進后的算法具有易編程,精確度更高的特點。并在此基礎(chǔ)上給出了完整的計算程序包,建立了目前最為完整的mathieu函數(shù)曲線庫。
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)是橢圓柱坐標系統(tǒng)下場論分析的基礎(chǔ),因此本文首先對mathieu函數(shù)的數(shù)值計算問題進行了詳細研究,并在前人基礎(chǔ)上完善并進一步改進了目前被認為較為可行的數(shù)值算法,并提出了驗證算法。
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)時存在一些困難,主要是因為不能簡單方便地對其進行解析表示,我們給出整數(shù)階各類馬丟函數(shù)的詳細計算方法,該方法適合較大范圍的階數(shù)n和參數(shù)q值,實際計算中采用了matlab軟件進行編程實現(xiàn),并給出了各類馬丟函數(shù)在自變量和q值兩個參數(shù)變化下的三維可視化圖形。