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

InhaltsverzeichnisI: 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.