Author | Reinhardt, H.-J. author |
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Title | Analysis of Approximation Methods for Differential and Integral Equations [electronic resource] / by H.-J. Reinhardt |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1985 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1080-1 |
Descript | 398p. online resource |
I: Presentation of Numerical Methods -- 1. Finite-Difference Methods for Boundary-Value Problems -- 2. Projection Methods for Variational Equations -- 3. Approximation Methods for Integral Equations of the Second Kind -- 4. Approximation Methods for Initial Value Problems in Partial Differential Equations 74 -- II: Convergence Theory -- 5. The Concepts of Discrete Convergence and Discrete Approximations -- 6. Discrete Convergence of Mappings and Solutions of Equations -- 7. Compactness Criteria for Discrete Convergence -- III: Convergence Analysis for Approximate Solutions of Boundary-Value Problems and Integral Equations -- 8. Convergence of Finite-Difference Methods for Boundary-Value Problems -- 9. Biconvergence for Projection Methods Via Variational Principles -- 10. Convergence of Perturbations of Integral Equations of The Second Kind -- IV: Inverse Stability, Consistency and Convergence for Initial Value Problems in Partial Differential Equations -- 11. Inverse Stability and Convergence for General Discrete-Time Approximations of Linear and Nonlinear Initial Value Problems -- 12. Special Criteria for Inverse Stability -- 13. Convergence Analysis of Special Methods -- Glossary of Symbols