Ebook: Defect Correction Methods: Theory and Applications

Ten years ago, the term "defect correction" was introduced to characterize a class of methods for the improvement of an approximate solution of an operator equation. This class includes many well-known techniques (e.g. Newton's method) but also some novel approaches which have turned out to be quite efficient. Meanwhile a large number of papers and reports, scattered over many journals and institutions, have appeared in this area. Therefore, a working conference on "Error Asymptotics and Defect Corrections" was organized by K. Bohmer, V. Pereyra and H. J. Stetter at the Mathematisches Forschungsinstitut Oberwolfach in July 1983, a meeting which aimed at bringing together a good number of the scientists who are active in this field. Altogether 26 persons attended, whose interests covered a wide spectrum from theoretical analyses to applications where defect corrections may be utilized; a list of the participants may be found in the Appendix. Most of the colleagues who presented formal lectures at the meeting agreed to publish their reports in this volume. It would be presumptuous to call this book a state-of-the-art report in defect corrections. It is rather a collection of snapshots of activities which have been going on in a number of segments on the frontiers of this area. No systematic coverage has been attempted. Some articles focus strongly on the basic concepts of defect correction; but in the majority of the contributions the defect correction ideas appear rather as instruments for the attainment of some specified goal.

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Content:
Front Matter....Pages I-IX
The Defect Correction Approach....Pages 1-32
Defect Correction Algorithms for Stiff Ordinary Differential Equations....Pages 33-41
On a Principle of Direct Defect Correction Based on A-Posteriori Error Estimates....Pages 43-66
Simultaneous Newton’s Iteration for the Eigenproblem....Pages 67-74
On Some Two-level Iterative Methods....Pages 75-87
Local Defect Correction Method and Domain Decomposition Techniques....Pages 89-113
Fast Adaptive Composite Grid (FAC) Methods: Theory for the Variational Case....Pages 115-121
Mixed Defect Correction Iteration for the Solution of a Singular Perturbation Problem....Pages 123-145
Solution of Linear and Nonlinear Algebraic Problems with Sharp, Guaranteed Bounds....Pages 147-168
Residual Correction and Validation in Functoids....Pages 169-192
Defect Corrections and Hartree-Fock Method....Pages 193-209
Deferred Corrections Software and Its Application to Seismic Ray Tracing....Pages 211-226
Numerical Engineering: Experiences in Designing PDE Software with Selfadaptive Variable Step Size/Variable Order Difference Methods....Pages 227-242
Back Matter....Pages 243-243

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Content:
Front Matter....Pages I-IX
The Defect Correction Approach....Pages 1-32
Defect Correction Algorithms for Stiff Ordinary Differential Equations....Pages 33-41
On a Principle of Direct Defect Correction Based on A-Posteriori Error Estimates....Pages 43-66
Simultaneous Newton’s Iteration for the Eigenproblem....Pages 67-74
On Some Two-level Iterative Methods....Pages 75-87
Local Defect Correction Method and Domain Decomposition Techniques....Pages 89-113
Fast Adaptive Composite Grid (FAC) Methods: Theory for the Variational Case....Pages 115-121
Mixed Defect Correction Iteration for the Solution of a Singular Perturbation Problem....Pages 123-145
Solution of Linear and Nonlinear Algebraic Problems with Sharp, Guaranteed Bounds....Pages 147-168
Residual Correction and Validation in Functoids....Pages 169-192
Defect Corrections and Hartree-Fock Method....Pages 193-209
Deferred Corrections Software and Its Application to Seismic Ray Tracing....Pages 211-226
Numerical Engineering: Experiences in Designing PDE Software with Selfadaptive Variable Step Size/Variable Order Difference Methods....Pages 227-242
Back Matter....Pages 243-243
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