Factorization of Boundary Value Problems Using the Invariant Embedding Method

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 problemsMakes a link between control theory, boundary value problems and the Gauss factorizationPresents a new theory for successively solving linear elliptic boundary value problemsIncludes a transformation in two initial value problems that are uncoupled

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