An introduction to computational stochastic PDEs:
This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes t...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2014
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| Schriftenreihe: | Cambridge texts in applied mathematics
50 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 TUM01 TUM02 Volltext |
| Zusammenfassung: | This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of-the-art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modelling and materials science |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xi, 503 pages) |
| ISBN: | 9781139017329 |
| DOI: | 10.1017/CBO9781139017329 |
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| 245 | 1 | 0 | |a An introduction to computational stochastic PDEs |c Gabriel J. Lord, Heriot-Watt University, Edinburgh, Catherine E. Powell, University of Manchester, Tony Shardlow, University of Bath |
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| 505 | 8 | |a Machine generated contents note: Part I. Deterministic Differential Equations: 1. Linear analysis; 2. Galerkin approximation and finite elements; 3. Time-dependent differential equations; Part II. Stochastic Processes and Random Fields: 4. Probability theory; 5. Stochastic processes; 6. Stationary Gaussian processes; 7. Random fields; Part III. Stochastic Differential Equations: 8. Stochastic ordinary differential equations (SODEs); 9. Elliptic PDEs with random data; 10. Semilinear stochastic PDEs | |
| 520 | |a This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of-the-art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modelling and materials science | ||
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Datensatz im Suchindex
| _version_ | 1804176881670422528 |
|---|---|
| any_adam_object | |
| author | Lord, Gabriel J. |
| author_facet | Lord, Gabriel J. |
| author_role | aut |
| author_sort | Lord, Gabriel J. |
| author_variant | g j l gj gjl |
| building | Verbundindex |
| bvnumber | BV043940761 |
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| classification_tum | MAT 606f |
| collection | ZDB-20-CBO |
| contents | Machine generated contents note: Part I. Deterministic Differential Equations: 1. Linear analysis; 2. Galerkin approximation and finite elements; 3. Time-dependent differential equations; Part II. Stochastic Processes and Random Fields: 4. Probability theory; 5. Stochastic processes; 6. Stationary Gaussian processes; 7. Random fields; Part III. Stochastic Differential Equations: 8. Stochastic ordinary differential equations (SODEs); 9. Elliptic PDEs with random data; 10. Semilinear stochastic PDEs |
| ctrlnum | (ZDB-20-CBO)CR9781139017329 (OCoLC)907964094 (DE-599)BVBBV043940761 |
| dewey-full | 519.2/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/2 |
| dewey-search | 519.2/2 |
| dewey-sort | 3519.2 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139017329 |
| format | Electronic eBook |
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| id | DE-604.BV043940761 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9781139017329 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349731 |
| oclc_num | 907964094 |
| open_access_boolean | |
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| owner_facet | DE-12 DE-92 DE-91G DE-BY-TUM |
| physical | 1 online resource (xi, 503 pages) |
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| publishDate | 2014 |
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| publisher | Cambridge University Press |
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| series2 | Cambridge texts in applied mathematics |
| spelling | Lord, Gabriel J. Verfasser aut An introduction to computational stochastic PDEs Gabriel J. Lord, Heriot-Watt University, Edinburgh, Catherine E. Powell, University of Manchester, Tony Shardlow, University of Bath Cambridge Cambridge University Press 2014 1 online resource (xi, 503 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge texts in applied mathematics 50 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Machine generated contents note: Part I. Deterministic Differential Equations: 1. Linear analysis; 2. Galerkin approximation and finite elements; 3. Time-dependent differential equations; Part II. Stochastic Processes and Random Fields: 4. Probability theory; 5. Stochastic processes; 6. Stationary Gaussian processes; 7. Random fields; Part III. Stochastic Differential Equations: 8. Stochastic ordinary differential equations (SODEs); 9. Elliptic PDEs with random data; 10. Semilinear stochastic PDEs This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of-the-art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modelling and materials science Stochastic partial differential equations MATLAB (DE-588)4329066-8 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd rswk-swf Stochastische partielle Differentialgleichung (DE-588)4135969-0 s Numerisches Verfahren (DE-588)4128130-5 s MATLAB (DE-588)4329066-8 s 1\p DE-604 Powell, Catherine E. Sonstige oth Shardlow, Tony Sonstige oth Erscheint auch als Druckausgabe 978-0-521-72852-2 Erscheint auch als Druckausgabe 978-0-521-89990-1 https://doi.org/10.1017/CBO9781139017329 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lord, Gabriel J. An introduction to computational stochastic PDEs Machine generated contents note: Part I. Deterministic Differential Equations: 1. Linear analysis; 2. Galerkin approximation and finite elements; 3. Time-dependent differential equations; Part II. Stochastic Processes and Random Fields: 4. Probability theory; 5. Stochastic processes; 6. Stationary Gaussian processes; 7. Random fields; Part III. Stochastic Differential Equations: 8. Stochastic ordinary differential equations (SODEs); 9. Elliptic PDEs with random data; 10. Semilinear stochastic PDEs Stochastic partial differential equations MATLAB (DE-588)4329066-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| subject_GND | (DE-588)4329066-8 (DE-588)4128130-5 (DE-588)4135969-0 |
| title | An introduction to computational stochastic PDEs |
| title_auth | An introduction to computational stochastic PDEs |
| title_exact_search | An introduction to computational stochastic PDEs |
| title_full | An introduction to computational stochastic PDEs Gabriel J. Lord, Heriot-Watt University, Edinburgh, Catherine E. Powell, University of Manchester, Tony Shardlow, University of Bath |
| title_fullStr | An introduction to computational stochastic PDEs Gabriel J. Lord, Heriot-Watt University, Edinburgh, Catherine E. Powell, University of Manchester, Tony Shardlow, University of Bath |
| title_full_unstemmed | An introduction to computational stochastic PDEs Gabriel J. Lord, Heriot-Watt University, Edinburgh, Catherine E. Powell, University of Manchester, Tony Shardlow, University of Bath |
| title_short | An introduction to computational stochastic PDEs |
| title_sort | an introduction to computational stochastic pdes |
| topic | Stochastic partial differential equations MATLAB (DE-588)4329066-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| topic_facet | Stochastic partial differential equations MATLAB Numerisches Verfahren Stochastische partielle Differentialgleichung |
| url | https://doi.org/10.1017/CBO9781139017329 |
| work_keys_str_mv | AT lordgabrielj anintroductiontocomputationalstochasticpdes AT powellcatherinee anintroductiontocomputationalstochasticpdes AT shardlowtony anintroductiontocomputationalstochasticpdes |