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An introduction to computational sto...

Lord, Gabriel J.

An introduction to computational stochastic PDEs /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	An introduction to computational stochastic PDEs /Gabriel J. Lord, Catherine E. Powell, Tony Shardlow.
其他題名:	Introduction to computational stochastic partial differential equations
作者:	Lord, Gabriel J.
其他作者:	Powell, Catherine E.
出版者:	New York, NY :Cambridge University Press,2014.
面頁冊數:	xi, 503 p. :ill. (some col.) ;26 cm.
標題:	Stochastic partial differential equations.
電子資源:	http://assets.cambridge.org/97805218/99901/cover/9780521899901.jpg
ISBN:	9780521899901 (hbk.) :

An introduction to computational stochastic PDEs /
Lord, Gabriel J.

An introduction to computational stochastic PDEs /Introduction to computational stochastic partial differential equationsGabriel J. Lord, Catherine E. Powell, Tony Shardlow. - New York, NY :Cambridge University Press,2014. - xi, 503 p. :ill. (some col.) ;26 cm. - Cambridge texts in applied mathematics ;50.

Includes bibliographical references (p. [489]-498) and index.

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 modeling and materials science"--

ISBN: 9780521899901 (hbk.) :NT$3533

LCCN: 2014005535Subjects--Topical Terms:

199002
Stochastic partial differential equations.

LC Class. No.: QA274.25 / .L67 2014

Dewey Class. No.: 519.2/2

An introduction to computational stochastic PDEs /
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008 150922s2014 nyua b 001 0 eng
010 $a 2014005535
020 $a 9780521899901 (hbk.) : $c NT$3533
020 $a 0521899907 (hbk.)
020 $a 9780521728522 (pbk.)
020 $a 0521728525 (pbk.)
035 $a 2014005535
040 $a DLC $b eng $c DLC $d DLC
042 $a pcc
050 0 0 $a QA274.25 $b .L67 2014
082 0 0 $a 519.2/2 $2 23
100 1 $a Lord, Gabriel J. $3 394268
245 1 3 $a An introduction to computational stochastic PDEs / $c Gabriel J. Lord, Catherine E. Powell, Tony Shardlow.
246 3 $a Introduction to computational stochastic partial differential equations
260 $a New York, NY : $b Cambridge University Press, $c 2014.
300 $a xi, 503 p. : $b ill. (some col.) ; $c 26 cm.
490 0 $a Cambridge texts in applied mathematics ; $v 50
504 $a Includes bibliographical references (p. [489]-498) and index.
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 modeling and materials science"-- $c Provided by publisher.
650 0 $a Stochastic partial differential equations. $3 199002
700 1 $a Powell, Catherine E. $3 709082
700 1 $a Shardlow, Tony. $3 709083
856 4 2 $3 Cover image $u http://assets.cambridge.org/97805218/99901/cover/9780521899901.jpg