Accession Number : AD0631190

Title :   LECTURES ON TOPICS IN NONLINEAR DIFFERENTIAL EQUATIONS,

Corporate Author : DAVID TAYLOR MODEL BASIN WASHINGTON D C APPLIED MATHEMATICS LAB

Personal Author(s) : Temple,G.

Report Date : MAR 1960

Pagination or Media Count : 50

Abstract : These lectures describe some recent researches by the author and one of his graduate students at Oxford University on ordinary nonlinear differential equations. The first lecture is devoted to a search for a 'superposition' principle for these nonlinear equations and it determines the class of nonlinear equations for which such a superposition principle exists. The remaining four lectures provide a rigorous, analytical theory of the technique invented by Lighthill (1949) for solving nonlinear differential equations with an 'irregular' perturbation. Such equations involve a small parameter alpha and such that the coefficient of the highest derivative vanishes identically, or at the 'initial point', when alpha = 0. The theory is developed from a number of simple examples and given a rigorous form by means of the theory of 'dominant functions'. (Author)

Descriptors :   (*NONLINEAR DIFFERENTIAL EQUATIONS, THEORY), NUMERICAL INTEGRATION, PERTURBATION THEORY

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE