Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering 1st Edition by Fabio Silva Botelho 9781000205879 1000205878

Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering 1st Edition Fabio Silva Botelho – Ebook Instant Download/Delivery ISBN(s): 9781000205879, 1000205878

Product details:

• ISBN 10: 1000205878
• ISBN 13:9781000205879
• Author: Fabio Silva Botelho

Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering

Table contents:

ormulation of the topology optimization problem
21.3 About the computational method
21.4 Computational simulations and results
21.5 Final remarks and conclusions
22. Existence and Duality Principles for the Ginzburg-Landau System in Superconductivity
22.1 Introduction
22.2 The main result
22.3 A second multi-duality principle
22.4 Another duality principle for global optimization
22.5 The existence of a global solution for the Ginzburg-Landau system in the presence of a magnetic
22.6 Duality for the complex Ginzburg-Landau system
22.7 Conclusion
23. Existence of Solution for an Optimal Control Problem Associated to the Ginzburg-Landau System in
23.1 Introduction
23.2 An existence result for a related optimal control problem
23.3 A method to obtain approximate numerical solutions for a class of partial differential equation
23.4 Conclusion
24. Duality for a Semi-Linear Model in Micro-Magnetism
24.1 Introduction
24.2 The duality principle for the semi-linear model
24.3 Conclusion
25. About Numerical Methods for Ordinary and Partial Differential Equations
25.1 Introduction
25.2 On the numerical procedures for Ginzburg-Landau type ODEs
25.3 Numerical results for related P.D.E.s
25.3.1 A related P.D.E on a special class of domains
25.3.2 About the matrix version of G.M.O.L.
25.3.3 Numerical results for the concerning partial differential equation
25.4 A proximal algorithm for optimization in Rn
25.4.1 The main result
25.5 Conclusion
26. On the Numerical Solution of First Order Ordinary Differential Equation Systems
26.1 Introduction
26.2 The main results
26.3 Numerical results
26.4 The Newton’s method for another first order system
26.4.1 An example in nuclear physics
26.5 Conclusion
27. On the Generalized Method of Lines and its Proximal Explicit and Hyper-Finite Difference Approac
27.1 Introduction
27.1.1 Some preliminaries results and the main algorithm
27.1.2 A numerical example, the proximal explicit approach
27.2 The hyper-finite differences approach
27.2.1 The main algorithm
27.2.2 A numerical example
27.3 Conclusion
28. On the Generalized Method of Lines Applied to the Time-Independent Incompressible Navier-Stokes
28.1 Introduction
28.2 On the solution of the time-independent incompressible Navier-Stokes system through an associat
28.3 The generalized method of lines for the Navier-Stokes system
28.3.1 Numerical examples through the generalized method of lines
28.4 Conclusion
29. A Numerical Method for an Inverse Optimization Problem through the Generalized Method of Lines
29.1 Introduction
29.2 The mathematical description of the main problem
29.3 About the generalized method of lines and the main result
29.3.1 The numerical results
29.4 Conclusion
30. A Variational Formulation for Relativistic Mechanics based on Riemannian Geometry and its Applic
30.1 Introduction
30.2 Some introductory topics on vector analysis and Riemannian geometry
30.3 A relativistic quantum mechanics action
30.3.1 The kinetics energy
30.3.2 The energy part relating the curvature and wave function
30.4 Obtaining the relativistic Klein-Gordon equation as an approximation of the previous action
30.5 A note on the Einstein field equations in the vacuum
30.6 Conclusion

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