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AbstractAbstract
[en] The aim of this report is to find, with a fair accuracy, a proper value λmn(c) for the spheroidal differential equation: d/dz[(1-z2)du/dz]+[ λ - c2z2 - m2/(1-z2)]u = 0 obtained by the separation of the three variables of the wave equation: Δ2u + k2u = 0 with rotational elongated or flattened ellipsoidal coordinates. The program drawn up calculates λmn(c) for any values of (mnc) chosen in the zones 0 ≤ | m | ≤ 10, a whole number; |m| ≤ n ≤ 20, n a whole number; 0 ≤ |c | ≤ 30; previous work has covered a smaller field of values. The function to be solved by the approximation method of the Newton-Raphson type, and the initial value, are chosen so as to converge towards the required solution. (author)
[fr]
L'objet de ce rapport est de rechercher avec une tres bonne approximation, une valeur propre λmn(c) de l'equation differentielle spheroidale: d/dz[(1-z2)du/dz]+[ λ - c2z2 - m2/1-z2]u = 0 obtenue par separation des 3 variables de l'equation des ondes: Δ2u + k2u = 0 en coordonnees des ellipsoides de revolution allonges ou aplatis. Le programme etabli calcule λmn(c) quel que soit le jeu (mnc) choisi dans le domaine 0 ≤ | m | ≤ 10 entier; |m| ≤ n ≤ 20, n entier; 0 ≤ |c | ≤ 30; alors que les etudes precedentes portaient sur un domaine plus restreint. La fonction a resoudre par la methode d'approximation du type NEWTON-RAPHSON et la valeur initiale, sont choisies de facon a converger vers la solution desiree. (auteur)Original Title
Calcul des valeurs propres λmn(c) de l'equation spheroidale
Primary Subject
Secondary Subject
Source
May 1969; [43 p.]; These calcul automatique, option calcul scientifique
Record Type
Report
Literature Type
Thesis/Dissertation
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