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An introduction to computational sto...

Lord, Gabriel J.

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An introduction to computational stochastic PDEs

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	An introduction to computational stochastic PDEs/ Gabriel J. Lord, Catherine E. Powell, Tony Shardlow.
作者:	Lord, Gabriel J.
其他作者:	Powell, Catherine E.
出版者:	Cambridge :Cambridge University Press, : 2014.,
面頁冊數:	xi, 503 p. :ill., digital ;24 cm.
內容註:	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.
標題:	Stochastic partial differential equations. -
電子資源:	https://doi.org/10.1017/CBO9781139017329
ISBN:	9781139017329

An introduction to computational stochastic PDEs
Lord, Gabriel J.

An introduction to computational stochastic PDEs[electronic resource] /Gabriel J. Lord, Catherine E. Powell, Tony Shardlow. - Cambridge :Cambridge University Press,2014. - xi, 503 p. :ill., digital ;24 cm. - Cambridge texts in applied mathematics ;50. - Cambridge texts in applied mathematics ;50..

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.

ISBN: 9781139017329Subjects--Topical Terms:

625093
Stochastic partial differential equations.

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

Dewey Class. No.: 519.22

An introduction to computational stochastic PDEs
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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.
650 0 $a Stochastic partial differential equations. $3 625093
700 1 $a Powell, Catherine E. $3 2144365
700 1 $a Shardlow, Tony. $3 2144366
830 0 $a Cambridge texts in applied mathematics ; $v 50. $3 3391767
856 4 0 $u https://doi.org/10.1017/CBO9781139017329