ABSTRACT
The book includes theoretical and applied results of a generalization of the numerical method of lines. A Ginzburg-Landau type equation comprises the initial application, with detailed explanations about the establishment of the general line expressions. Approximate numerical procedures have been developed for a variety of equation types, including the related algorithms and software. The applications include the Ginzburg-Landau system in superconductivity, applications to the Navier-Stokes system in fluid mechanics and, among others, models in flight mechanics. In its second and final parts, the book develops duality principles and numerical results for other similar and related models.
The book is meant for applied mathematicians, physicists and engineers interested in numerical methods and concerning duality theory. It is expected the text will serve as a valuable auxiliary project tool for some important engineering and physics fields of research.
TABLE OF CONTENTS
part I|72 pages
The Generalized Method of Lines
chapter Chapter 1|24 pages
The Generalized Method of Lines Applied to a Ginzburg-Landau Type Equation
chapter Chapter 2|11 pages
An Approximate Proximal Numerical Procedure Concerning the Generalized Method of Lines
chapter Chapter 3|29 pages
Approximate Numerical Procedures for the Navier-Stokes System through the Generalized Method of Lines
part II|138 pages
Calculus of II Variations, Convex Analysis and Restricted Optimization
part III|93 pages
Duality Principles and Related Numerical Examples through the Generalized Method of Lines