ODE/PDE Analysis of Multiple Myeloma, Schiesser, William
Автор: Schiesser, W.e. (lehigh University, Bethlehem, Pennsylvania, Usa) Название: Time delay ode/pde models ISBN: 0367427974 ISBN-13(EAN): 9780367427979 Издательство: Taylor&Francis Рейтинг: Цена: 117390.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The intent of this book is to present a methodology for the formulation and computer implementation of mathematical models based on time delay ordinary differential equations (DODEs) and partial differential equations (DPDEs) in biomedical science and engineering (BMSE).
Автор: Vande Wouwer, Alain Saucez, Philippe Vilas Fernandez, Carlos Название: Simulation of ode/pde models with matlab, octave and scilab ISBN: 3319067893 ISBN-13(EAN): 9783319067896 Издательство: Springer Рейтинг: Цена: 149060.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Simulation of ODE/PDE Models with MATLAB(R), OCTAVE and SCILAB
Автор: Habib Ammari, Yves Capdeboscq, Hyeonbae Kang Название: Multi-Scale and High-Contrast PDE: From Modelling, to Mathematical Analysis, to Inversion ISBN: 0821869299 ISBN-13(EAN): 9780821869291 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 61910.00 T Наличие на складе: Невозможна поставка. Описание: This volume contains the proceedings of the conference “Multi-Scale and High-Contrast PDE: From Modelling, to Mathematical Analysis, to Inversion'', held June 28-July 1, 2011, at the University of Oxford.<br><br> The mathematical analysis of PDE modelling materials, or tissues, presenting multiple scales has been an active area of research for more than 40 years. The study of the corresponding imaging, or reconstruction, problem is a more recent one. If the material parameters of the PDE present high contrast ratio, then the solution to the PDE becomes particularly challenging to analyse, or compute. Similar difficulties occur in time dependent equations in high frequency regimes. Over the last decade the analysis of the inversion problem at moderate frequencies, the rigourous derivation of asymptotics at high frequencies, and the regularity properties of solutions of elliptic PDE in highly heterogeneous media have received a lot of attention.<br><br> The focus of this volume is on recent progress towards a complete understanding of the direct problem with high contrast or high frequencies, and unified approaches to the inverse and imaging problems for both small and large contrast or frequencies. The volume also includes contributions on the inverse problem, both on its analysis and on numerical reconstructions. It offers the reader a good overview of current research and direction for further pursuit on multiscale problems, both in PDE and in signal processing, and in the analysis of the equations or the computation of their solutions. Special attention is devoted to new models and problems coming from physics leading to innovative imaging methods.
Автор: William Schiesser Название: Moving Boundary PDE Analysis: Biomedical Applications in R ISBN: 0367224836 ISBN-13(EAN): 9780367224837 Издательство: Taylor&Francis Рейтинг: Цена: 117390.00 T Наличие на складе: Невозможна поставка. Описание: The book is directed to the numerical integration (solution) of systems of partial differential equations (PDEs) for which the boundary conditions move in space. In applications, the physical boundaries move as the solution evolves in time. The book provides examples of the applications in tumor growth and atherosclerosis
Автор: William E. Schiesser Название: Numerical Pde Analysis of the Blood Brain Barrier: Method of Lines in R ISBN: 9813275790 ISBN-13(EAN): 9789813275799 Издательство: World Scientific Publishing Рейтинг: Цена: 95040.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
The remarkable functionality of the brain is made possible by the metabolism (chemical reaction) of oxygen (O₂) and nutrients in the brain. These metabolism components are supplied to the brain by an intricate blood circulatory system (vasculature). The blood brain barrier (BBB), which is the central topic of this book, determines the rate of transfer from the blood to the brain tissue.
In particular, mathematical models are developed for mass transfer across the BBB based on partial differential equations (PDEs) applied to the blood capillaries, the endothelial membrane, and the brain tissue. The PDEs derived from mass balances and computer routines in R are presented for the numerical (computer-based) solution of the PDEs. The computed concentration profiles of the transferred components are functions of time and space within the BBB system, i.e., spatiotemporal solutions.
The R routines and the associated numerical algorithms for computing the numerical solutions are discussed in detail. The discussion is introductory, without formal mathematics, e.g., theorems and proofs. The general methodology (algorithm) for numerical PDE solutions is the method of lines (MOL).
The models are used to study the transfer of oxygen and nutrients, harmful substances that should not enter the brain such as chemicals and pathogens (viruses, bacteria), and therapeutic drugs. The intent of the book is to provide a quantitative approach to the study of BBB dynamics using a computer-based methodology programmed in R, a quality open-source scientific programming system that is easily downloaded from the Internet for execution on modest computers.
Автор: William Schiesser Название: PDE Analysis of the Blood Brain Barrier: Method of Lines in R ISBN: 3110612453 ISBN-13(EAN): 9783110612455 Издательство: Walter de Gruyter Цена: 133830.00 T Наличие на складе: Нет в наличии. Описание: This book discusses the computer-based implementation of prototype partial differential equation models for the dynamics of mass transfer across the blood brain barrier. The numerical algorithm for the solution of PDE models is termed the method of lines. Numerical and graphical output from this model is presented with a discussion of possible application to neurodynamics.
Автор: Schiesser, W. E. Название: Schiesser-Numerical PDE Analysis of Retinal ISBN: 0128184523 ISBN-13(EAN): 9780128184523 Издательство: Elsevier Science Рейтинг: Цена: 129130.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Numerical PDE Analysis of Retinal Neovascularization Mathematical Model Computer Implementation in R provides a methodology for the analysis of neovascularization (formation of blood capillaries) in the retina. It describes the starting point-a system of three partial differential equations (PDEs)-that define the evolution of (1) capillary tip density, (2) blood capillary density and (3) concentration of vascular endothelial growth factor (VEGF) in the retina as a function of space (distance along the retina), x, and time, t, the three PDE dependent variables for (1), (2) and (3), and designated as u1(x, t), u2(x, t), u3(x, t), amongst other topics.
Includes PDE routines based on the method of lines (MOL) for computer-based implementation of PDE models
Offers transportable computer source codes for readers in R, with line-by-line code descriptions as it relates to the mathematical model and algorithms
Authored by a leading researcher and educator in PDE models
Автор: Martinsson, Per-gunnar Название: Fast direct solvers for elliptic pdes ISBN: 1611976030 ISBN-13(EAN): 9781611976038 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 72730.00 T Наличие на складе: Невозможна поставка. Описание: Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE.This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques.Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.
Автор: Boling Guo, Hongjun Gao, Xueke Pu Название: Stochastic PDEs and Dynamics ISBN: 3110495104 ISBN-13(EAN): 9783110495102 Издательство: Walter de Gruyter Рейтинг: Цена: 123910.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book explains mathematical theories of a collection of stochastic partial differential equations and their dynamical behaviors. Based on probability and stochastic process, the authors discuss stochastic integrals, Ito formula and Ornstein-Uhlenbeck processes, and introduce theoretical framework for random attractors. With rigorous mathematical deduction, the book is an essential reference to mathematicians and physicists in nonlinear science. Contents: PreliminariesThe stochastic integral and It formulaOU processes and SDEsRandom attractorsApplicationsBibliographyIndex
Автор: Massimo Cicognani; Ferruccio Colombini; Daniele De Название: Studies in Phase Space Analysis with Applications to PDEs ISBN: 148999940X ISBN-13(EAN): 9781489999405 Издательство: Springer Рейтинг: Цена: 139750.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book covers advances in linear and nonlinear aspects of the theory of partial differential equations. Includes general theory; Hardy-type inequalities; linear and non-linear hyperbolic equations; Schrodinger equations; water-wave equations and more.
Автор: Karl K. Sabelfeld, Irina A. Shalimova Название: Spherical and Plane Integral Operators for PDEs: Construction, Analysis, and Applications ISBN: 3110315297 ISBN-13(EAN): 9783110315295 Издательство: Walter de Gruyter Рейтинг: Цена: 185890.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.
Автор: Lord Название: An Introduction to Computational Stochastic PDEs ISBN: 0521728525 ISBN-13(EAN): 9780521728522 Издательство: Cambridge Academ Рейтинг: Цена: 60190.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 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 (R) codes are included, so that readers can perform computations themselves and solve the test problems discussed.
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