Numerical Methods for Stochastic Partial Differential Equations with White Noise, Zhongqiang Zhang; George Em Karniadakis
Автор: Oksendal Название: Stochastic Differential Equations ISBN: 3540047581 ISBN-13(EAN): 9783540047582 Издательство: Springer Рейтинг: Цена: 8223.00 р. Наличие на складе: Есть (1 шт.) Описание: Gives an introduction to the basic theory of stochastic calculus and its applications. This book offers examples in order to motivate and illustrate the theory and show its importance for many applications in for example economics, biology and physics.
Автор: Platen Название: Numerical Solution of Stochastic Differential Equations with Jumps in Finance ISBN: 3642120571 ISBN-13(EAN): 9783642120572 Издательство: Springer Рейтинг: Цена: 12717.00 р. 18167.00-30% Наличие на складе: Есть (1 шт.) Описание: It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability.
Описание: This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where the random walks live not only on the boundary, but also inside the domain. A variety of examples from capacitance calculations to electron dynamics in semiconductors are discussed to illustrate the viability of the approach.The book is written for mathematicians who work in the field of partial differential and integral equations, physicists and engineers dealing with computational methods and applied probability, for students and postgraduates studying mathematical physics and numerical mathematics. Contents: IntroductionRandom walk algorithms for solving integral equationsRandom walk-on-boundary algorithms for the Laplace equationWalk-on-boundary algorithms for the heat equationSpatial problems of elasticityVariants of the random walk on boundary for solving stationary potential problemsSplitting and survival probabilities in random walk methods and applicationsA random WOS-based KMC method for electron-hole recombinationsMonte Carlo methods for computing macromolecules properties and solving related problemsBibliography
Описание: This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equations. It uses a unique teaching method which explains the analysis using exercises and detailed solutions.
Описание: The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations.
Описание: The computational solution of partial differential systems has become so involved that it is important to automate decisions that have been left to the individual. This book covers such decisions: mesh generation with links to the software generating the domain geometry; and solution accuracy with mesh selection linked to solution generation.
Автор: Ahmad Shair Название: Textbook on Ordinary Differential Equations ISBN: 3319164074 ISBN-13(EAN): 9783319164076 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available.
Описание: The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations.
Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs
This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along.
Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book:
Discusses various methods for solving linear and nonlinear ODEs and PDEs
Covers basic numerical techniques for solving differential equations along with various discretization methods
Investigates nonlinear differential equations using semi-analytical methods
Examines differential equations in an uncertain environment
Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations
Contains solved example problems, as well as some unsolved problems for self-validation of the topics covered
Advanced Numerical and Semi Analytical Methods for Differential Equations is an excellent text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically.
Описание: This graduate textbook - now in its second edition - teaches finite element methods and basic finite difference methods from a computational point of view. The emphasis is on developing flexible computer programs using the numerical library Diffpack. Diffpack is explained in detail for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. All the program examples, as well as Diffpack for use with this book, are available on the Internet.
Описание: A matrix oriented introduction to domain decomposition methodology. It discusses topics including hybrid formulations, Schwarz, substructuring and Lagrange multiplier methods for elliptic equations, computational issues, least squares-control methods, multilevel methods, non-self adjoint problems, parabolic equations and saddle point applications.
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