The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering

SECTION I: THE GENERALIZED METHOD OF LINES. The Generalized Method of Lines Applied to a Ginzburg-Landau Type Equation. An Approximate Proximal Numerical Procedure Concerning the Generalized Method of Lines. Approximate Numerical Procedures for the Navier-Stokes System through the Generalized Method of Lines. An Approximate Numerical Method for Ordinary Differential Equation Systems with Applications to a Flight Mechanics Model. SECTION II: CALCULUS OF VARIATIONS, CONVEX ANALYSIS AND RESTRICTED OPTIMIZATION. Basic Topics on the Calculus of Variations. More topics on the Calculus of Variations. Convex Analysis and Duality Theory. Constrained Variational Optimization. On Lagrange Multiplier Theorems for Non-Smooth Optimization for a Large Class of Variational Models in Banach Spaces. SECTION III: DUALITY PRINCIPLES AND RELATED NUMERICAL EXAMPLES THROUGH THE ENERALIZED METHOD OF LINES. A Convex Dual Formulation for a Large Class of Non-Convex Models in Variational Optimization. Duality Principles and Numerical Procedures for a Large Class of Non-Convex Models in the Calculus of Variations. Dual Variational Formulations for a Large Class of Non-Convex Models in the Calculus of Variations. A Note on the Korn's Inequality in a n-Dimensional Context and a Global Existence Result for a Non-Linear Plate Model. References.