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This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.
List of contents
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.
About the author
Gabriel Lord is a Professor in the Maxwell Institute, Department of Mathematics, at Heriot-Watt University, Edinburgh. He has worked on stochastic PDEs and applications for the past ten years. He is the co-editor of Stochastic Methods in Neuroscience with C. Liang, has organised a number of international meetings in the field, and is principal investigator on the porous media processes and mathematics network funded by the Engineering and Physical Sciences Research Council (UK). He is a member of the Society for Industrial and Applied Mathematics, LMS, and EMS, as well as an Associate Editor for the SIAM Journal on Scientific Computing and the SIAM/ASA Journal on Uncertainty Quantification.
Summary
This comprehensive introduction to stochastic partial differential equations incorporates the effects of randomness into real-world models, offering graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. MATLAB® codes are included, so that readers can perform computations themselves and solve the test problems discussed.
