Nonclassical linear Volterra equations of the first kind:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Utrecht [u.a.]
VSP
2003
|
| Edition: | 1. publ. |
| Series: | Inverse and ill-posed problems series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 168 S. |
| ISBN: | 9067643750 |
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MARC
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Record in the Search Index
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| adam_text | INVERSE AND ILL-POSED PROBLEMS SERIES NONCLASSICAL LINEAR VO I TERRA
EQUATIONS OF THE FIRST KIND A.S. APARTSYN III MSP III UTRECHT * BOSTON
2003 CONTENTS INTRODUCTION 1 CHAPTER 1. CLASSICAL VOLTERRA EQUATIONS OF
THE FIRST KIND 5 1.1. CLASSIFICATION OF INTEGRAL VOLTERRA EQUATIONS OF
THE FIST KIND . . . . 5 1.2. THE GRONWALL-BELLMAN LEMMA 10 1.3. A
DIFFERENCE ANALOG OF THE GRONWALL-BELLMAN LEMMA 14 1.4.
SELF-REGULARIZATION 17 1.5. TWO-PARAMETRIC (A, /I)-REGULARIZATION 19
1.6. INEQUALITIES WITH ISOTONE OPERATORS 32 1.7. INEQUALITIES WITH
INTERCHANGEABLE ISOTONE OPERATORS 39 1.8. UNIMPROVABLE ESTIMATES OF
SOLUTIONS OF MULTIDIMENSIONAL INTEGRAL INEQUALITIES 43 1.9. THE
WELL-POSEDNESS OF A TWO-DIMENSIONAL VOLTERRA EQUATION OF THE FIRST KIND
49 1.10. UNIMPROVABLE ESTIMATES OF SOLUTIONS OF TWO-DIMENSIONAL DIFFER-
ENCE INEQUALITIES 51 CHAPTER 2. VOLTERRA EQUATIONS OF THE FIRST KIND
WITH TWO VARIABLE INTEGRATION LIMITS. THE CASE A(TO) TO 57 2.1.
PROBLEM STATEMENT 57 2.2. THE METHOD OF STEPS 58 2.3. ILLUSTRATIVE
EXAMPLES 62 2.4. THE EXISTENCE AND UNIQUENESS THEOREM 65 2.5. AN
ESTIMATE OF THE SOLUTION STABILITY 68 2.6. THE STUDY OF A SPECIAL
PROBLEM OF MATHEMATICAL PROGRAMMING . . 70 VIII A.S. APARTSYN.
NONCLASSICAL LINEAR VOLTERRA EQUATIONS ... 2.7. A NUMERICAL SOLUTION OF
THE TEST EXAMPLE 79 2.8. A GEOMETRICAL ILLUSTRATION OF THE REDUCTION BY
UNITY IN THE ORDER OF CONVERGENCE 81 2.9. A THEOREM ON THE CONVERGENCE
OF THE QUADRATURE METHOD (THE GENERAL CASE) 84 2.10. SOME NUMERICAL
RESULTS 90 2.11. ON SELF-REGULARIZATION 96 CHAPTER 3. VOLTERRA EQUATIONS
OF THE FIRST KIND WITH TWO VARIABLE LIMITS OF INTEGRATION. THE CASE
A(TO) = TO 99 3.1. PROBLEM STATEMENT 99 3.2. SOLUTION OF THE SIMPLEST
TEST EQUATION 100 3.3. EXISTENCE AND UNIQUENESS THEOREM (THE GENERAL
CASE) 102 3.4. ESTIMATION OF THE SOLUTION STABILITY 104 3.5. SOME
GENERALIZATIONS OF THE GRONWALL-BELLMAN INEQUALITY 107 3.6. NUMERICAL
SOLUTION OF A TEST EXAMPLE 114 3.7. THE PROOF OF CONVERGENCE FOR THE
QUADRATURE METHOD (THE GENERAL CASE) . . 118 3.8. SOME NUMERICAL RESULTS
124 3.9. SELF-REGULARIZATION (THE CASE OF A DISTURBANCE IN THE
RIGHT-HAND SIDE) 126 3.10. STABILITY OF A NUMERICAL SOLUTION WITH
RESPECT TO DISTURBANCES OF A(T) 128 3.11. MULTIDIMENSIONAL VOLTERRA
EQUATIONS OF THE FIRST KIND RELATED TO THE MODELLING OF NONLINEAR
DYNAMIC SYSTEMS USING THE VOLTERRA SERIES 130 BIBLIOGRAPHY 155 INDEX 167
|
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| discipline | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV017404981 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:17:39Z |
| institution | BVB |
| isbn | 9067643750 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010489012 |
| oclc_num | 52048440 |
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| physical | VIII, 168 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | VSP |
| record_format | marc |
| series2 | Inverse and ill-posed problems series |
| spelling | Apartsyn, A. S. Verfasser aut Nonclassical linear Volterra equations of the first kind A. S. Apartsyn 1. publ. Utrecht [u.a.] VSP 2003 VIII, 168 S. txt rdacontent n rdamedia nc rdacarrier Inverse and ill-posed problems series Volterra equations Volterra-Gleichungen (DE-588)4137459-9 gnd rswk-swf Volterra-Gleichungen (DE-588)4137459-9 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010489012&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Apartsyn, A. S. Nonclassical linear Volterra equations of the first kind Volterra equations Volterra-Gleichungen (DE-588)4137459-9 gnd |
| subject_GND | (DE-588)4137459-9 |
| title | Nonclassical linear Volterra equations of the first kind |
| title_auth | Nonclassical linear Volterra equations of the first kind |
| title_exact_search | Nonclassical linear Volterra equations of the first kind |
| title_full | Nonclassical linear Volterra equations of the first kind A. S. Apartsyn |
| title_fullStr | Nonclassical linear Volterra equations of the first kind A. S. Apartsyn |
| title_full_unstemmed | Nonclassical linear Volterra equations of the first kind A. S. Apartsyn |
| title_short | Nonclassical linear Volterra equations of the first kind |
| title_sort | nonclassical linear volterra equations of the first kind |
| topic | Volterra equations Volterra-Gleichungen (DE-588)4137459-9 gnd |
| topic_facet | Volterra equations Volterra-Gleichungen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010489012&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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