The asymptotic behaviour of nonoscillatory solutions of second order nonlinear ordinary differential equations is studied. Necessary and sufficient conditions are given for the existence of positive solutions with specified asymptotic behaviour at infinity. Existence of nonoscillatory solutions is established using the Schauder-Tychonoff fixed point theorem. Techniques such as factorization of linear disconjugate operators are employed to reveal the similar nature of asymptotic solutions of nonlinear differential equations to that of linear equations. Some examples illustrating the asymptotic theory of ordinary differential equations are given. / Science, Faculty of / Mathematics, Department of / Graduate

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Meteorology, 1979. / Microfiche copy available in Archives and Science. / Bibliography : leaves 71-72. / by Jon Alan Pollack. / M.S.

The Spectral method is a powerful numerical technique for solving engineering differential equations. The method is a specialization of the method of weighted residuals. Trial functions that are easily and exactly differentiable are used. Often the functions used also satisfy an orthogonality equation, which can improve the efficiency of the approximation. Generally, the entire domain is modeled, but multiple sub-domains may be used. A Chebyshev-Collocation Spectral method is used to solve a variety of ordinary and partial differential equations. The Chebyshev Polynomial series follows a well established recursion relation for calculation of the polynomials and their derivatives. Two different schemes are studied for formulation of the problems, a Fast Fourier Transform approach, and a matrix multiplication approach. First, the one-dimensional ordinary differential equation representing the deflection of a tapered bar under its own weight is studied. Next, the two dimensional Poisson's equation is examined. Lastly, a two dimensional, highly non-linear, two parameter Bratu's equation is solved. Each problem's results are compared to results from other methods or published data. Accuracy is very good, with a significant improvement in computer time. / Master of Science

Call number: LD2668 .T4 1985 B78 / Master of Science

Thesis (B.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1978. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 110-111. / B.S.

Wang, Yuqian. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 36-39). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Properties of approximate solutions --- p.6 / Chapter 3 --- Liapunov-Schmidt Reduction --- p.17 / Chapter 4 --- Critical point of the reduced energy functional --- p.28 / Bibliography --- p.36

He Yiran. / Includes index. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (p. 74-80) and index.. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Abstract not available

For thesis abstract select View Thesis Title, Contents and Abstract

Bibliography: p.109-111. / Contract DA36-030-AMC-03200(E).