Scaling of Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Scaling of Differential Equations write by Hans Petter Langtangen. This book was released on 2016-06-15. Scaling of Differential Equations available in PDF, EPUB and Kindle. The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.
The Method of Intrinsic Scaling
The Method of Intrinsic Scaling - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Method of Intrinsic Scaling write by José Miguel Urbano. This book was released on 2008-05-20. The Method of Intrinsic Scaling available in PDF, EPUB and Kindle. This set of lectures, which had its origin in a mini course delivered at the Summer Program of IMPA (Rio de Janeiro), is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular PDEs.In the first part, the theory is presented from scratch for the model case of the degenerate p-Laplace equation. The second part deals with three applications of the theory to relevant models arising from flows in porous media and phase transitions.
Handbook of Differential Equations
Handbook of Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Handbook of Differential Equations write by Daniel Zwillinger. This book was released on 1998. Handbook of Differential Equations available in PDF, EPUB and Kindle. This book compiles the most widely applicable methods for solving and approximating differential equations. as well as numerous examples showing the methods use. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations. For nearly every technique, the book provides: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users References to the literature for more discussion or more examples, including pointers to electronic resources, such as URLs
Applied Stochastic Differential Equations
Applied Stochastic Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Applied Stochastic Differential Equations write by Simo Särkkä. This book was released on 2019-05-02. Applied Stochastic Differential Equations available in PDF, EPUB and Kindle. With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Applications of Dynamical Systems in Biology and Medicine
Applications of Dynamical Systems in Biology and Medicine - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Applications of Dynamical Systems in Biology and Medicine write by Trachette Jackson. This book was released on 2015-07-06. Applications of Dynamical Systems in Biology and Medicine available in PDF, EPUB and Kindle. This volume highlights problems from a range of biological and medical applications that can be interpreted as questions about system behavior or control. Topics include drug resistance in cancer and malaria, biological fluid dynamics, auto-regulation in the kidney, anti-coagulation therapy, evolutionary diversification and photo-transduction. Mathematical techniques used to describe and investigate these biological and medical problems include ordinary, partial and stochastic differentiation equations, hybrid discrete-continuous approaches, as well as 2 and 3D numerical simulation.
