Stochastic Numerics for Mathematical Physics

Stochastic differential equations have many applications in the natural sciences. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce solution of multi-dimensional problems for partial differential equations to integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. The authors propose many new special schemes, some published here for the first time. In the second part of the book they construct numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.

Author: Grigori N. Milstein, Michael V. Tretyakov
Publisher: Springer
Published: 12/05/2022
Pages: 736
Binding Type: Paperback
Weight: 2.32lbs
Size: 9.21h x 6.14w x 1.52d
ISBN: 9783030820428

About the Author
Professor G.N. Milstein received his undergraduate degree in mathematics from the Ural State University (UrGU; Sverdlovsk, USSR), which is now Ural Federal University (Ekaterinburg, Russia). He completed his PhD studies at the same University. Professor Milstein has been an assistant professor, associate professor and, after defending his DSc thesis, professor at the Faculty of Mathematics and Mechanics of UrGU (then URFU). For a number of years, he worked as a senior researcher at the Weierstrass Institute for Applied Analysis and Stochastics (WIAS; Berlin, Germany). He was also a Visiting Professor at the University of Leicester (UK) and the University of Manchester (UK). Professor Milstein has a world-leading expertise in stochastic numerics, estimation, control, stability, financial mathematics. Milstein's early pioneering papers on numerical methods for stochastic differential equations are the cornerstones of the modern stochastic numerics.Professor M.V. Tretyakov received his undergraduate degree in mathematics from the Ural State University (UrGU; Sverdlovsk, USSR). He completed his PhD studies at the same University.
Professor Tretyakov has gained experience in stochastic numerics during his stay at the Weierstrass Institute for Applied Analysis and Stochastics (WIAS, Berlin) as a DAAD Research Fellow and then a Research Fellow of the Alexander von Humboldt Foundation. He worked as senior researcher at the Institute of Mathematics and Mechanics (Russian Academy of Sciences, Ekaterinburg) and at UrGU. He was a lecturer at Swansea University (UK) and a lecturer, reader and professor at the University of Leicester (UK). Since 2012 he is a professor at the University of Nottingham (UK). He has served on editorial boards of numerical analysis and scientific computing journals. His research has been supported by the Leverhulme Trust, EPSRC, BBSRC, and Royal Society. Professor Tretyakov has extensive world-class expertise in stochastic numerical analysis. He also conducts high quality research in financial mathematics, stochastic dynamics, and uncertainty quantification.