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Instabilities in numerical solutions to Fredholm and Volterra integral equations of the first kind. Resolution by Tchebycheff polynomials. Application to photonuclear cross-sections; Instabilite des solutions numeriques d'equations integrales de Fredholm et Volterra de premiere espece. Resolution par les polynomes de Tchebycheff. Application aux sections efficaces photonucleaires

Abstract

It is well known, if not well explained, that photo cross-sections curves depend on numerical resolution; as well as many other physical solutions from integral equations of the first kind, they are oscillating. In the first part of this report, a typical example points out how oscillations are growing. In the second part, a new method is explained yielding a smooth resolution. From experimental data on equidistant intervals, we build functions expanded in Tchebycheff polynomials; the solution is of this kind. Then, the third part points out that semi-analytical resolutions of this problem are illusive. (author) [French] C'est un fait reconnu mais mal explique, que les courbes de sections efficaces photonucleaires dependent de la resolution numerique adoptee. Beaucoup d'autres solutions physiques extraites d'une equation integrale de 1ere espece sont dans ce cas; elles sont arbitraires et oscillatoires. Dans la 1ere partie de ce rapport, on montre, dans un cas particulier typique, comment se forment les oscillations. Dans la 2eme partie, on presente une methode originale qui permet d'obtenir une resolution exempte d'oscillations. A partir de donnees experimentales a intervalles equidistants, on construit des fonctions developpees en polynomes de Tchebycheff; la solution est de ce type. Enfin, on montre dans la  More>>
Authors:
Moriceau, Y [1] 
  1. Commissariat a l'Energie Atomique, Centre d'Etudes de Limeil, 94 - Villeneuve-Saint-Georges (France)
Publication Date:
Mar 01, 1968
Product Type:
Technical Report
Report Number:
CEA-R-3427
Resource Relation:
Other Information: 32 refs; PBD: Mar 1968
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BETHE-HEITLER THEORY; BREMSSTRAHLUNG; CROSS SECTIONS; ELECTRON BEAMS; FOURIER ANALYSIS; FREDHOLM EQUATION; LEAST SQUARE FIT; NUMERICAL SOLUTION; OSCILLATIONS; PHOTON BEAMS; PHOTONUCLEAR REACTIONS; POLYNOMIALS; VOLTERRA INTEGRAL EQUATIONS
OSTI ID:
20523249
Research Organizations:
CEA Saclay, 91 - Gif-sur-Yvette (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR04R3427091304
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
[47] pages
Announcement Date:
Dec 10, 2004

Citation Formats

Moriceau, Y. Instabilities in numerical solutions to Fredholm and Volterra integral equations of the first kind. Resolution by Tchebycheff polynomials. Application to photonuclear cross-sections; Instabilite des solutions numeriques d'equations integrales de Fredholm et Volterra de premiere espece. Resolution par les polynomes de Tchebycheff. Application aux sections efficaces photonucleaires. France: N. p., 1968. Web.
Moriceau, Y. Instabilities in numerical solutions to Fredholm and Volterra integral equations of the first kind. Resolution by Tchebycheff polynomials. Application to photonuclear cross-sections; Instabilite des solutions numeriques d'equations integrales de Fredholm et Volterra de premiere espece. Resolution par les polynomes de Tchebycheff. Application aux sections efficaces photonucleaires. France.
Moriceau, Y. 1968. "Instabilities in numerical solutions to Fredholm and Volterra integral equations of the first kind. Resolution by Tchebycheff polynomials. Application to photonuclear cross-sections; Instabilite des solutions numeriques d'equations integrales de Fredholm et Volterra de premiere espece. Resolution par les polynomes de Tchebycheff. Application aux sections efficaces photonucleaires." France.
@misc{etde_20523249,
title = {Instabilities in numerical solutions to Fredholm and Volterra integral equations of the first kind. Resolution by Tchebycheff polynomials. Application to photonuclear cross-sections; Instabilite des solutions numeriques d'equations integrales de Fredholm et Volterra de premiere espece. Resolution par les polynomes de Tchebycheff. Application aux sections efficaces photonucleaires}
author = {Moriceau, Y}
abstractNote = {It is well known, if not well explained, that photo cross-sections curves depend on numerical resolution; as well as many other physical solutions from integral equations of the first kind, they are oscillating. In the first part of this report, a typical example points out how oscillations are growing. In the second part, a new method is explained yielding a smooth resolution. From experimental data on equidistant intervals, we build functions expanded in Tchebycheff polynomials; the solution is of this kind. Then, the third part points out that semi-analytical resolutions of this problem are illusive. (author) [French] C'est un fait reconnu mais mal explique, que les courbes de sections efficaces photonucleaires dependent de la resolution numerique adoptee. Beaucoup d'autres solutions physiques extraites d'une equation integrale de 1ere espece sont dans ce cas; elles sont arbitraires et oscillatoires. Dans la 1ere partie de ce rapport, on montre, dans un cas particulier typique, comment se forment les oscillations. Dans la 2eme partie, on presente une methode originale qui permet d'obtenir une resolution exempte d'oscillations. A partir de donnees experimentales a intervalles equidistants, on construit des fonctions developpees en polynomes de Tchebycheff; la solution est de ce type. Enfin, on montre dans la 3eme partie que les resolutions semi-analytiques de ce probleme sont illusoires. (auteur)}
place = {France}
year = {1968}
month = {Mar}
}