The splitting extrapolation method: a new technique in numerical solution of multidimensional problems
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1995
|
| Series: | Series on applied mathematics
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 316 S. graph. Darst. |
| ISBN: | 9810222173 |
Staff View
MARC
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| 100 | 1 | |a Liem, Chin-bo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The splitting extrapolation method |b a new technique in numerical solution of multidimensional problems |c C. B. Liem ; T. Lü ; T. M. Shih |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1995 | |
| 300 | |a XIX, 316 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series on applied mathematics |v 7 | |
| 650 | 7 | |a Extrapolation |2 ram | |
| 650 | 4 | |a Splitting extrapolation method | |
| 650 | 0 | 7 | |a Multivariate Approximation |0 (DE-588)4314108-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Extrapolation |0 (DE-588)4153421-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Multivariate Approximation |0 (DE-588)4314108-0 |D s |
| 689 | 0 | 1 | |a Extrapolation |0 (DE-588)4153421-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Lü, Tao |e Verfasser |4 aut | |
| 700 | 1 | |a Shih, Tsimin |e Verfasser |4 aut | |
| 830 | 0 | |a Series on applied mathematics |v 7 |w (DE-604)BV007228284 |9 7 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
Acknowledgements vii
Introduction ix
List of symbols xiii
I. Generalization and application of Richardson s extrapola¬
tion 1
1. Polynomial extrapolation 1
1.1. Interpolation polynomials and extrapolation 2
1.2. Polynomial extrapolation algorithms and their generalization 5
1.3. Stability and convergence 9
1.4. A posteriori error estimation 15
2. Application in numerical integration 20
2.1. Euler Maclaurin summation formulae 20
2.2. Euler Maclaurin formulae for integrands with singularities
at end points 29
2.3. Multidimensional Euler Maclaurin expansion 31
2.4. Asymptotic expansion of multidimensional numerical quad¬
rature of functions with singularities 33
2.5. Numerical results 39
II. Splitting Extrapolation Methods 43
1. Multivariate asymptotic expansion 45
2. Recurrence algorithm of splitting extrapolation 47
3. Coefficients and stability of SEM 51
4. A posteriori error estimation of splitting extrapolation 59
5. Fractional power expansion and successive elimination methods. 61
III. Application of SEM to multidimensional numerical inte¬
gration 69
1. Splitting extrapolation algorithms for smooth functions 70
2. Change of variables of multidimensional improper integrals 79
3. Duffy transform for multidimensional improper integrals 83
4. Multivariate asymptotic expansion of multidimensional improper
integrals 85
xvii
xviii Contents
5. Integration on multidimensional simplexes 90
6. Integration on multidimensional domains with curved boundaries 96
IV. SEM for integral equations 99
1. General theory of integral operators 99
2. Approximate quadrature methods 105
3. SEM for multidimensional integral equations with smooth
kernels 109
4. SEM for integral equations in polygonal domains 114
5. SEM for eigenvalues and eigenfunctions 125
6. SEM for integral equations with nonsmooth kernels 132
7. SEM for collocation method solutions of one dimensional weakly
singular integral equations 143
8. SEM for collocation method solutions of multidimensional
weakly singular integral equations 153
V. SEM for differential equations 159
1. SEM for the collocation method solutions of two point boundary
value problems 160
1.1. SEM for the collocation method solutions of the quasilinear
two point boundary value problems 160
1.2. SEM for the collocation method solutions of Sturm Liouville
type eigenvalue problems 163
1.3. SEM for singular two point boundary value problems 168
1.4. SEM for two point boundary value problems with discon¬
tinuous coefficients 170
2. SEM for finite difference approximations 172
2.1. Difference equations and the discrete maximum principle.... 172
2.2. Multivariate asymptotic expansion of the finite difference
approximation on a domain with a smooth boundary 178
2.3. Multivariate asymptotic expansion of the finite difference
approximation on a rectangular parallelepiped 189
2.4. Numerical examples 196
3. SEM for finite element approximations 200
3.1. Finite element approximations of second order elliptic
equations 201
3.2. Basic expansion of bilinear rectangular elements 204
3.3. Expansion of three dimensional problems 217
3.4. Piecewise uniform rectangular partition and multiparameter
asymptotic expansion 223
3.5. Piecewise strongly regular partition 227
3.6. Numerical examples 230
Contents xix
VI. Combination methods for accelerating the convergence .. 232
1. Combination methods 232
1.1. Combination principle 232
1.2. Combination methods for integral equations 234
1.3. Combination methods for difference equations 236
2. Combination methods for collocation method solutions of
quadratic and cubic splines 241
3. Combination methods for the Nystrom solution of boundary
integral equations of the second kind 247
3.1. Boundary integral equations of the second kind 247
3.2. Combination methods for the Nystrom solutions 248
3.3. The nonsmooth cases 253
3.4. Neumann boundary value problems 255
3.5. Numerical examples 257
VII. Sparse grid methods and combination techniques 260
1. Sparse grids 261
1.1. Multilevel splitting of finite element spaces 261
1.2. Two dimensional sparse grids 265
1.3. Higher dimensional sparse grids 268
1.4. Finite element equations on a sparse grid 271
2. Combination techniques z
2.1. Two dimensional combination techniques 274
2.2. Three dimensional combination techniques 276
2.3. Numerical examples 280
2.4. Comparison of combination techniques, SEM and sparse
grid methods
3. Outline of the implicit extrapolation 290
Appendices 293
Bibliography 303
Index 313
|
| any_adam_object | 1 |
| author | Liem, Chin-bo Lü, Tao Shih, Tsimin |
| author_facet | Liem, Chin-bo Lü, Tao Shih, Tsimin |
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| building | Verbundindex |
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| callnumber-label | QA297 |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)32510685 (DE-599)BVBBV012739349 |
| dewey-full | 519.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4 |
| dewey-search | 519.4 |
| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012739349 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:32:51Z |
| institution | BVB |
| isbn | 9810222173 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008662669 |
| oclc_num | 32510685 |
| open_access_boolean | |
| owner | DE-703 DE-11 |
| owner_facet | DE-703 DE-11 |
| physical | XIX, 316 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on applied mathematics |
| series2 | Series on applied mathematics |
| spelling | Liem, Chin-bo Verfasser aut The splitting extrapolation method a new technique in numerical solution of multidimensional problems C. B. Liem ; T. Lü ; T. M. Shih Singapore [u.a.] World Scientific 1995 XIX, 316 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on applied mathematics 7 Extrapolation ram Splitting extrapolation method Multivariate Approximation (DE-588)4314108-0 gnd rswk-swf Extrapolation (DE-588)4153421-9 gnd rswk-swf Multivariate Approximation (DE-588)4314108-0 s Extrapolation (DE-588)4153421-9 s DE-604 Lü, Tao Verfasser aut Shih, Tsimin Verfasser aut Series on applied mathematics 7 (DE-604)BV007228284 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008662669&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Liem, Chin-bo Lü, Tao Shih, Tsimin The splitting extrapolation method a new technique in numerical solution of multidimensional problems Series on applied mathematics Extrapolation ram Splitting extrapolation method Multivariate Approximation (DE-588)4314108-0 gnd Extrapolation (DE-588)4153421-9 gnd |
| subject_GND | (DE-588)4314108-0 (DE-588)4153421-9 |
| title | The splitting extrapolation method a new technique in numerical solution of multidimensional problems |
| title_auth | The splitting extrapolation method a new technique in numerical solution of multidimensional problems |
| title_exact_search | The splitting extrapolation method a new technique in numerical solution of multidimensional problems |
| title_full | The splitting extrapolation method a new technique in numerical solution of multidimensional problems C. B. Liem ; T. Lü ; T. M. Shih |
| title_fullStr | The splitting extrapolation method a new technique in numerical solution of multidimensional problems C. B. Liem ; T. Lü ; T. M. Shih |
| title_full_unstemmed | The splitting extrapolation method a new technique in numerical solution of multidimensional problems C. B. Liem ; T. Lü ; T. M. Shih |
| title_short | The splitting extrapolation method |
| title_sort | the splitting extrapolation method a new technique in numerical solution of multidimensional problems |
| title_sub | a new technique in numerical solution of multidimensional problems |
| topic | Extrapolation ram Splitting extrapolation method Multivariate Approximation (DE-588)4314108-0 gnd Extrapolation (DE-588)4153421-9 gnd |
| topic_facet | Extrapolation Splitting extrapolation method Multivariate Approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008662669&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007228284 |
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