Solution of differential equations by means of one-parameter groups:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boston ; London ; Melbourne
Pitman Advanced Publishing Program
1982
|
| Schriftenreihe: | Research Notes in Mathematics
63 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000143712&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | 161 Seiten |
| ISBN: | 0273085069 0858968932 |
Internformat
MARC
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| 100 | 1 | |a Hill, James Madison |0 (DE-588)115749868X |4 aut | |
| 245 | 1 | 0 | |a Solution of differential equations by means of one-parameter groups |c J M Hill ; University of Wollongong |
| 264 | 1 | |a Boston ; London ; Melbourne |b Pitman Advanced Publishing Program |c 1982 | |
| 300 | |a 161 Seiten | ||
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| 490 | 1 | |a Research Notes in Mathematics |v 63 | |
| 650 | 4 | |a Groupes, Théorie des | |
| 650 | 4 | |a Équations différentielles - Solutions numériques | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Group theory | |
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Datensatz im Suchindex
| _version_ | 1819293822770741248 |
|---|---|
| adam_text | Contents
1. Introduction 1
1.1 Ordinary differential equations 1
1.2 Partial differential equations 6
Problems 9
2. One parameter groups and Lie series 12
2.1 One parameter transformation groups 12
2.2 Lie series and the commutation theorem 18
Problems 21
3. Invarianoe of standard linear equations 26
3.1 First order equation y + p(x)y = q(x) 26
3.2 Second order homogeneous equation y + p(x)y =0 30
3.3 Third order homogeneous equation y + p(x)y + q(x)y = 0 33
3.4 Fourth order self adjoint equation y + [p(x)y ] + q(x)y =0 36
Problems 39
4. First order differential equations 48
4.1 Infinitesimal versions of y and y = F(x,y) and the
fundamental problem 49
4.2 Integrating factors and canonical coordinates for y = F(x,y) 51
4.3 The alternative problem 55
4.4 The fundamental problem and singular solutions of y = F(x,y) 58
4.5 Invariance of the associated first order partial differential
equation 59
4.6 Lie s problem and area preserving groups 62
Problems 66
5. Second and higher order differencial equations 11
5.1 Infinitesimal versions of y and y = F(x,y,y ) 77
5.2 Examples of the determination of £(x,y) and r|(x,y) 79
5.3 Determination of the most general differential equation
invariant under a given one parameter group 83
5.4 Applications 87
Problems 92
6. Linear partial differential equations 97
6.1 Formulae for partial derivatives 99
6.2 Classical groups for the diffusion equation 101
6.3 Simple examples for the diffusion equation 103
6.4 Moving boundary problems 105
6.5 Fokker Planck equation 109
6.6 Examples for the Fokker Planck equation 116
6.7 Non classical groups for the diffusion equation 120
Problems 123
7. Non linear partial differential equations 135
7.1 Formulae for partial derivatives 136
7.2 Classical groups for non linear diffusion 140
7.3 Non classical groups for non linear diffusion 146
7.4 Transformations of the non linear diffusion equation 148
Problems 150
References 159
|
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| ctrlnum | (OCoLC)8218940 (DE-599)BVBBV000239351 |
| dewey-full | 515.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/5 |
| dewey-search | 515.3/5 |
| dewey-sort | 3515.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000239351 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T07:17:47Z |
| institution | BVB |
| isbn | 0273085069 0858968932 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000143712 |
| oclc_num | 8218940 |
| open_access_boolean | |
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| owner_facet | DE-12 DE-384 DE-355 DE-BY-UBR DE-824 DE-83 DE-188 |
| physical | 161 Seiten |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Pitman Advanced Publishing Program |
| record_format | marc |
| series | Research Notes in Mathematics |
| series2 | Research Notes in Mathematics |
| spellingShingle | Hill, James Madison Solution of differential equations by means of one-parameter groups Research Notes in Mathematics Groupes, Théorie des Équations différentielles - Solutions numériques Differential equations Numerical solutions Group theory Gruppentheorie (DE-588)4072157-7 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4012249-9 |
| title | Solution of differential equations by means of one-parameter groups |
| title_auth | Solution of differential equations by means of one-parameter groups |
| title_exact_search | Solution of differential equations by means of one-parameter groups |
| title_full | Solution of differential equations by means of one-parameter groups J M Hill ; University of Wollongong |
| title_fullStr | Solution of differential equations by means of one-parameter groups J M Hill ; University of Wollongong |
| title_full_unstemmed | Solution of differential equations by means of one-parameter groups J M Hill ; University of Wollongong |
| title_short | Solution of differential equations by means of one-parameter groups |
| title_sort | solution of differential equations by means of one parameter groups |
| topic | Groupes, Théorie des Équations différentielles - Solutions numériques Differential equations Numerical solutions Group theory Gruppentheorie (DE-588)4072157-7 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Groupes, Théorie des Équations différentielles - Solutions numériques Differential equations Numerical solutions Group theory Gruppentheorie Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000143712&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000039 |
| work_keys_str_mv | AT hilljamesmadison solutionofdifferentialequationsbymeansofoneparametergroups |