Factorization of Boundary Value Problems Using the Invariant Embedding Method

ISBN-13: 9781785481437 / Angielski / Twarda / 2016 / 256 str.

Jacques Henry

Opis

Factorization Method for Boundary Value Problems by Invariant Embedding presents a new theory for linear elliptic boundary value problems. The authors provide a transformation of the problem in two initial value problems that are uncoupled, enabling you to solve these successively. This method appears similar to the Gauss block factorization of the matrix, obtained in finite dimension after discretization of the problem. This proposed method is comparable to the computation of optimal feedbacks for linear quadratic control problems.

• Develops the invariant embedding technique for boundary value problems
• Makes a link between control theory, boundary value problems and the Gauss factorization
• Presents a new theory for successively solving linear elliptic boundary value problems
• Includes a transformation in two initial value problems that are uncoupled

Spis treści

1: Presentation of the Formal Computation of Factorization

2: Justification of the Factorization Computation

3: Complements to the Model Problem

4: Interpretation of the Factorization through a Control Problem

5: Factorization of the Discretized Problem

6: Other Problems

7: Other Shapes of Domain

8: Factorization by the QR Method

9: Representation Formulas for Solutions of Riccati Equations

O autorze

Jacques Henry is Director of Research, emeritus at INRIA Bordeaux Sud-ouest, France. He graduated from E´cole Polytechnique, Paris (1970). He has worked within INRIA (National Institute for Computer Sciences and Automatic Control, France) since 1974. His work covers control of systems governed by partial differential equations, modeling, parameter estimation and continuation-bifurcation methods applied to biological systems mainly in cardiac electrophysiology and biological sequences comparison. His current interests are on numerical analysis, inverse problems and singular perturbations for partial differential equations. He is developing research on the method of factorization of linear elliptic boundary value problems in terms of product of Cauchy problems. He was leading the INRIA project team Anubis on structured population dynamics. He has a special interest on the evolution of activity of popula- tions of neurons. His research is focused on modeling, optimization and simulation in Science and Technology, mainly using Partial Differential Equations. His research lines are the following: Epidemic modeling, spatial-stochastic individual based models, SIR models, hybrid models, risk analysis, validation with real data, control measures, economic and climate change impact analysis. He received his PhD. in Applied Mathematics from UCM< in July 1996. He is Director of the UCM Research Group Mathematical Models in Science and Engineering: Development, Analysis, Numerical Simulation and Control (MOMAT) since 2005.