Numerical solution of nonlinear boundary value problems with applications:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Englewood Cliffs
Prentice-Hall
1983
|
| Schriftenreihe: | Prentice-Hall international series in the physical and chemical engineering sciences.
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001372788&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | X, 323 S. Ill., graph. Darst. |
| ISBN: | 0136273645 |
Internformat
MARC
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| 100 | 1 | |a Kubiček, Milan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Numerical solution of nonlinear boundary value problems with applications |c Milan Kubiček ; Vladimir Hlaváček |
| 264 | 1 | |a Englewood Cliffs |b Prentice-Hall |c 1983 | |
| 300 | |a X, 323 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Prentice-Hall international series in the physical and chemical engineering sciences. | |
| 650 | 4 | |a Engineering mathematics |v Formulae | |
| 650 | 4 | |a Nonlinear boundary value problems | |
| 650 | 4 | |a Numerical calculations | |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Hlavacek, Vladimir |e Verfasser |0 (DE-588)126486727 |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001372788&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 667f 2001 A 21511 |
|---|---|
| DE-BY-TUM_katkey | 256615 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010427297 |
| _version_ | 1821934670704541697 |
| adam_text | Contents
Preface ix
1. Occurrence and Solution of Nonlinear Boundary
Value Problems in Engineering and Physics 1
1.1 Occurrence of nonlinear problems for ordinary
differential equations 1
1.2 Existence of a solution 2
1.3 Problems of a multiplicity of solutions 3
1.4 Nonlinear phenomena 3
1.5 Types of nonlinear boundary value problems in
chemical engineering 6
1.6 Types of nonlinear boundary value problems in physics 8
References 9
2. Initial and Boundary Value Problems for Ordinary
Differential Equations, Solution of Algebraic
Equations 11
2.1 Numerical solution of initial value problems 11
2.1.1 A short summary of commonly used methods, 12
v
v Contents
2.1.2 One step methods: Runge Kutta methods, 13
2.1.3 Linear multistep methods, 17
2.1.4 Numerical solution of stiff initial value
problems, 19
2.2 Dependence of solution of initial value problems on the
initial condition and on a parameter 22
2.3 Numerical solution of linear and nonlinear algebraic
equations 25
2.3.1 Gaussian elimination and its modifications, 25
2.3.2 Band and almost band matrices, 26
2.3.3 Solution of a single transcendental equation, 26
2.3.4 Solution of systems of nonlinear equations, 27
2.3.5 Dependence of the solution of a set of nonlinear
equations on a parameter, 33
2.4 Boundary value problems 34
2.4.1 Existence and uniqueness of solution, 34
2.4.2 Two point boundary value problem
of the pth order, 37
Bibliography 38
3. Linear Boundary Value Problems 41
3.1 Finite difference methods 41
3.2 Superposition of solution: Method of complementary
functions 49
3.3 Method of adjoints 55
3.4 Method of splitting the differential operator: the
factorization method 57
3.5 Invariant imbedding approach 63
3.6 Discussion 65
Problems 68
Bibliography 70
4. Numerical Methods for Nonlinear Boundary
Value Problems 72
4.1 Finite difference methods 72
4.1.1 Construction of the finite difference analogy, 73
4.1.2 Finite difference methods using approximations of
higher order, 75
4.1.3 Aspects of the effective use of finite difference
methods, 86
Contents vii
4.1.4 Numerical solution of finite difference
equations, 89
4.1.5 Remarks on the relative merits of the
finite difference technique, 94
Problems 95
Bibliography 97
4.2 Method of Green s functions 99
4.2.1 Construction of a Green s function, 99
4.2.2 Method of successive approximations, 102
4.2.3 Newton Kantorovich linearization, 103
4.2.4 Discussion, 108
Problems 109
Bibliography 110
4.3 Newton Kantorovich method and the quasi
linearization technique 110
4.3.1 Newton Kantorovich method, 111
4.3.2 Third order Newton Kantorovich method, 119
4.3.3 Discussion, 123
Problems 126
Bibliography 128
4.4 Method of false transient for the solution of
nonlinear boundary value problems 129
4.4.1 Introduction, 129
4.4.2 False transient equations, 130
4.4.3 Numerical solution of false transient
equations, 131
4.4.4 Examples, 135
4.4.5 Discussion, 151
Problems 152
Bibliography 153
4.5 One parameter imbedding technique 154
4.5.1 Introduction, 154
4.5.2 Details of one parameter imbedding
technique, 154
4.5.3 Continuous version of the Newton Kantorovich
method for NBVP, 161
4.5.4 Multiloop one parameter imbedding for the
NBVP, 166
4.5.5 One loop one parameter imbedding procedure for
the NBVP, 175
4.5.6 Numerical aspects of methods, 179
4.5.7 Discussion, 184
Problems 195
Bibliography 198
Viii Contents
4.6 Shooting methods 199
4.6.1 Problem of order 1, 200
4.6.2 Problems of higher order, 205
4.6.3 Discussion, 217
Problems 227
Bibliography 232
5. Numerical Realization of Parametric Studies in
Nonlinear Boundary Value Problems 234
5.1 Conversion of boundary value problems to initial value
problems and parameter mapping techniques 235
5.2 Sequential use of standard methods 253
5.3 Method of parametric differentiation 259
5.3.1 Description of the method, 259
5.3.2 Numerical realization of the method, 260
5.3.3 Examples, 270
5.4 Method of differentiation with respect to boundary
conditions 275
5.5 General parameter mapping technique 280
5.5.1 GPM algorithm for one second order
equation, 280
5.5.2 GPM algorithm for two second order
equations, 284
5.5.3 Predictor corrector GPM algorithm for two
second order equations, 289
5.5.4 GPM algorithm for a system of first order
differential equations, 296
5.6 Evaluation of branching points in nonlinear boundary
value problems 302
5.6.1 Branching points for one second order
equation, 303
5.6.2 Branching points for two second order
equations, 306
5.6.3 Branching points for a system of nonlinear
algebraic equations, 309
5.6.4 Branching points for a system of first order
differential equations, 311
Problems 314
Bibliography 318
Index 321
|
| any_adam_object | 1 |
| author | Kubiček, Milan Hlavacek, Vladimir |
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| classification_rvk | SK 915 SK 920 |
| classification_tum | MAT 673f MAT 667f |
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| dewey-full | 515.3/52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/52 |
| dewey-search | 515.3/52 |
| dewey-sort | 3515.3 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002094853 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T07:45:58Z |
| institution | BVB |
| isbn | 0136273645 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001372788 |
| oclc_num | 8282803 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-739 DE-29T DE-83 DE-11 DE-188 |
| owner_facet | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-739 DE-29T DE-83 DE-11 DE-188 |
| physical | X, 323 S. Ill., graph. Darst. |
| psigel | TUB-nveb |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Prentice-Hall |
| record_format | marc |
| series2 | Prentice-Hall international series in the physical and chemical engineering sciences. |
| spellingShingle | Kubiček, Milan Hlavacek, Vladimir Numerical solution of nonlinear boundary value problems with applications Engineering mathematics Formulae Nonlinear boundary value problems Numerical calculations Numerisches Verfahren (DE-588)4128130-5 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4048395-2 |
| title | Numerical solution of nonlinear boundary value problems with applications |
| title_auth | Numerical solution of nonlinear boundary value problems with applications |
| title_exact_search | Numerical solution of nonlinear boundary value problems with applications |
| title_full | Numerical solution of nonlinear boundary value problems with applications Milan Kubiček ; Vladimir Hlaváček |
| title_fullStr | Numerical solution of nonlinear boundary value problems with applications Milan Kubiček ; Vladimir Hlaváček |
| title_full_unstemmed | Numerical solution of nonlinear boundary value problems with applications Milan Kubiček ; Vladimir Hlaváček |
| title_short | Numerical solution of nonlinear boundary value problems with applications |
| title_sort | numerical solution of nonlinear boundary value problems with applications |
| topic | Engineering mathematics Formulae Nonlinear boundary value problems Numerical calculations Numerisches Verfahren (DE-588)4128130-5 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Engineering mathematics Formulae Nonlinear boundary value problems Numerical calculations Numerisches Verfahren Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001372788&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kubicekmilan numericalsolutionofnonlinearboundaryvalueproblemswithapplications AT hlavacekvladimir numericalsolutionofnonlinearboundaryvalueproblemswithapplications |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 667f 2001 A 21511
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |