Published November 13, 1969
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Research of the relations between the asymptotical behaviours of the solutions of a linear differential equation with polynomial coefficients in the neighbourhood of the singular points of the equation
Creators
- 1. Centre d'Etudes Nucleaires de Saclay, Direction des Piles Atomiques, Departement de Calcul Electronique (France)
Description
We consider the linear differential equation of order n: Lz(y)≡ Σk=0n pk(z) y(n-k) (z) = 0 (1), where the pk(z) are polynomials in z. The general problem we are interested in is to find the asymptotical behaviour of a given solution of (1) when z is in the neighbourhood of any singular point. - Recall about the Laplace integration method. - Application of the Laplace method when the pk(z) are linear functions in z. - Application to the equations (a) and (b): μy'''+ i z y'' + μ (1-α) y' + i (z-α/δ)y = 0 (a) (z2 + β2)y'' + (z2 -αz + β)y = 0 (b). (author)
Abstract (French)
Introduction: Nous considerons l'equation differentielle lineaire d'ordre n: Lz(y)≡ Σk=0n pk(z) y(n-k) (z) = 0 (1), ou les pk(z) sont des polynomes en z. Le probleme general qui nous interesse est de determiner le comportement asymptotique d'une solution donnee de (1) lorsque z se trouve dans le voisinage de tout point singulier. - Rappel de la methode d'integration de LAPLACE. - Application de la methode de LAPLACE au cas ou les pk(z) sont des fonctions lineaires de z. - Application aux equations (a) et (b): μy'''+ i z y'' + μ (1-α) y' + i (z-α/δ)y = 0 (a) (z2 + β2)y'' + (z2 -αz + β)y = 0 (b). (auteur)Files
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Additional details
Additional titles
- Original title (French)
- Recherche des relations entre les comportements asymptotiques des solutions d'une equation differentielle lineaire a coefficients polynomiaux au voisinage des points singuliers de l'equation
Publishing Information
- Imprint Pagination
- 46 p.
- Report number
- CEA-N--1240
INIS
- Country of Publication
- France
- Country of Input or Organization
- France
- INIS RN
- 49079499
- Subject category
- S97: MATHEMATICAL METHODS AND COMPUTING; S70: PLASMA PHYSICS AND FUSION TECHNOLOGY;
- Descriptors DEI
- ANALYTICAL SOLUTION; ASYMPTOTIC SOLUTIONS; DIFFERENTIAL OPERATORS; HANKEL TRANSFORM; INTEGRALS; LAGRANGE EQUATIONS; LAPLACE TRANSFORMATION; PLASMA WAVES; POLYNOMIALS; SINGULARITY; WAVE PROPAGATION
- Descriptors DEC
- DIFFERENTIAL EQUATIONS; EQUATIONS; FUNCTIONS; INTEGRAL TRANSFORMATIONS; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS; PARTIAL DIFFERENTIAL EQUATIONS; TRANSFORMATIONS
Optional Information
- Notes
- 4 refs.; Available from the INIS Liaison Officer for France, see the INIS website for current contact and E-mail addresses