Refined Iterative Methods for Computation of the Solution and the Eigenvalues of Self-Adjoint Boundary Value Problems

Inhaltsverzeichnis

• I: The Self-Adjoint Boundary Value Problem.
• 1. Problems of Dirichlet’s and Poisson’s type.
• 2. Better approximations.
• 3. Energy on the boundary.
• 4. Eigenvalue problems.
• 5. Biharmonic problems.
• 6. Adaption for practical purposes; the test example.
• 7. Modes of oscillation of the plate.
• II: Theory of Gradient Methods.
• 1. Introduction.
• 2. The residual polynomial.
• 3. Methods with two-term recursive formulae.
• 4. Methods with three-term recursive formulae.
• 5. Combined methods.
• 6. The cgT-method.
• 7. Determination of eigenvalues.
• III: Experiments on Gradient Methods.
• 2. Survey of the plate experiments.
• 3. Solution of the system A x + b = 0 (Plate problem with coarse grid).
• 4. Determination of the eigenvalues of A.
• 5. Solution of the system A x + b =0 and determination of the eigenvalues of A; fine grid.
• 6. Second test example: the bar problem.
• 7. Appendix: The first three eigenvectors of A.
• IV: Overrelaxation.
• 1. Theory.
• 2. Numerical results (Plate problem).
• 3. The bar problem.
• V: Conclusions.
• 1. The plate problem.
• 2. The bar problem.
• 3. Computation of eigenvalues.
• 4. Recollection of the facts.
• References.