Umfang:
Online-Ressource
,
v.: digital
Ausgabe:
Online-Ausg. Springer eBook Collection. Mathematics and Statistics Electronic reproduction; Available via World Wide Web
ISBN:
128335554X
,
9783034801072
,
9781283355544
Serie:
International Series of Numerical Mathematics 159
Inhalt:
Myroslav V. Kutniv
Inhalt:
The book provides a comprehensive introduction to compact finite difference methods for solving boundary value ODEs with high accuracy. The corresponding theory is based on exact difference schemes (EDS) from which the implementable truncated difference schemes (TDS) are derived. The TDS are now competitive in terms of efficiency and accuracy with the well-studied numerical algorithms for the solution of initial value ODEs. Moreover, various a posteriori error estimators are presented which can be used in adaptive algorithms as important building blocks. The new class of EDS and TDS treated in
Anmerkung:
Includes bibliographical references and index
,
Exact and Truncated Difference Schemes for Boundary Value ODEs; Contents; Preface; Chapter 1 Introduction and a short historical overview; 1.1 BVPs, Grids, Differences, Difference Schemes; 1.2 Short history; Chapter 2 Two-point difference schemes for systems of nonlinear BVPs; 2.1 Existence and uniqueness of the solution; 2.2 Existence of a two-point EDS; 2.3 Implementation of the 2-point EDS; 2.4 A posteriori error estimation and automatic grid generation; Chapter 3 Three-point difference schemes for monotone second-order ODEs; 3.1 Existence and uniqueness of a solution
,
3.2 Existence of a three-point EDS3.3 Implementation of the three-point EDS; 3.4 Boundary conditions of 3rd kind; 3.5 Numerical examples; Chapter 4 Three-point difference schemes for systems of monotone second-order ODEs; 4.1 Problem setting; 4.2 Existence of a three-point EDS; 4.3 Implementation of the three-point EDS; 4.4 Numerical examples; Chapter 5 Difference schemes for nonlinear BVPs on the half-axis; 5.1 Existence and uniqueness of the solution; 5.2 Existence of a three-point EDS; 5.3 Implementation of the three-point EDS; 5.4 Numerical examples; Chapter 6 Exercises and solutions
,
6.1 Exercises6.2 Solutions; Index; Bibliography
,
Electronic reproduction; Available via World Wide Web
Weitere Ausg.:
ISBN 1283355531
Weitere Ausg.:
ISBN 9783034801065
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Randwertproblem
;
Gewöhnliche Differentialgleichung
;
Differenzenverfahren
DOI:
10.1007/978-3-0348-0107-2
URL:
Volltext
(lizenzpflichtig)
Mehr zum Autor:
Hermann, Martin 1949-
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