# 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