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.
1. 5.1 Introduction and problem statement - p. 99 2. 5.2 Application of the factorization method to problem (Ph) - p. 102 3. 5.3 A second method of discretization - p. 108 4. 5.4 A third possibility: centered scheme - p. 111 5. 5.5 Row permutation - p. 114 6. 5.6 Case of a discretization of the section by finite elements - p. 118 7. 6: Other Problems - p. 127 8. Abstract - p. 127 9. 6.1 General second-order linear elliptic problems - p. 127 10. 6.2 Systems of coupled boundary value problems - p. 133 11. 6.3 Linear elasticity system - p. 141 12. 6.4 Problems of order higher than 2 - p. 149 13. 6.5 Stokes problems - p. 155 14. 6.6 Parabolic problems - p. 163 15. 7: Other Shapes of Domain - p. 169 16. 8: Factorization by the QR Method - p. 197 17. 9: Representation Formulas for Solutions of Riccati Equations - p. 213 18. Appendix: Gaussian LU Factorization as a Method of Invariant Embedding - p. 221 19. Bibliography - p. 233 20. Index - p. 237
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.
1. 5.1 Introduction and problem statement - p. 99 2. 5.2 Application of the factorization method to problem (Ph) - p. 102 3. 5.3 A second method of discretization - p. 108 4. 5.4 A third possibility: centered scheme - p. 111 5. 5.5 Row permutation - p. 114 6. 5.6 Case of a discretization of the section by finite elements - p. 118 7. 6: Other Problems - p. 127 8. Abstract - p. 127 9. 6.1 General second-order linear elliptic problems - p. 127 10. 6.2 Systems of coupled boundary value problems - p. 133 11. 6.3 Linear elasticity system - p. 141 12. 6.4 Problems of order higher than 2 - p. 149 13. 6.5 Stokes problems - p. 155 14. 6.6 Parabolic problems - p. 163 15. 7: Other Shapes of Domain - p. 169 16. 8: Factorization by the QR Method - p. 197 17. 9: Representation Formulas for Solutions of Riccati Equations - p. 213 18. Appendix: Gaussian LU Factorization as a Method of Invariant Embedding - p. 221 19. Bibliography - p. 233 20. Index - p. 237
