Accession Number:

AD0631190

Title:

LECTURES ON TOPICS IN NONLINEAR DIFFERENTIAL EQUATIONS,

Descriptive Note:

Corporate Author:

DAVID TAYLOR MODEL BASIN WASHINGTON D C APPLIED MATHEMATICS LAB

Personal Author(s):

Report Date:

1960-03-01

Pagination or Media Count:

50.0

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

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE