Numerical Methods For Random Ordinary Differential Equations And Their Applications In Biology And Medicine

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Numerical Methods For Random Ordinary Differential Equations And Their Applications In Biology And Medicine

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Author : Yusuke Asai
language : en
Publisher:
Release Date : 2016

Numerical Methods For Random Ordinary Differential Equations And Their Applications In Biology And Medicine written by Yusuke Asai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.

Random Ordinary Differential Equations And Their Numerical Solution

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Author : Xiaoying Han
language : en
Publisher: Springer
Release Date : 2017-10-25

Random Ordinary Differential Equations And Their Numerical Solution written by Xiaoying Han and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-25 with Mathematics categories.

This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs). RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems. They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor expansions in the usual sense. However, Taylor-like expansions can be derived for RODEs using an iterated application of the appropriate chain rule in integral form, and represent the starting point for the systematic derivation of consistent higher order numerical schemes for RODEs. The book is directed at a wide range of readers in applied and computational mathematics and related areas as well as readers who are interested in the applications of mathematical models involving random effects, in particular in the biological sciences.The level of this book is suitable for graduate students in applied mathematics and related areas, computational sciences and systems biology. A basic knowledge of ordinary differential equations and numerical analysis is required.

Nbs Special Publication

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Author :
language : en
Publisher:
Release Date : 1968

Nbs Special Publication written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Weights and measures categories.

Fractional Calculus

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Author : Dumitru Baleanu
language : en
Publisher: World Scientific
Release Date : 2012

Fractional Calculus written by Dumitru Baleanu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

This title will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods.

Modeling And Differential Equations In Biology

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Author : T. A. Burton
language : en
Publisher: Routledge
Release Date : 2017-10-05

Modeling And Differential Equations In Biology written by T. A. Burton and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-05 with Mathematics categories.

First published in 1980. CRC Press is an imprint of Taylor & Francis.

Modeling With It Stochastic Differential Equations

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Author : E. Allen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-08

Modeling With It Stochastic Differential Equations written by E. Allen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-08 with Mathematics categories.

Dynamical systems with random influences occur throughout the physical, biological, and social sciences. By carefully studying a randomly varying system over a small time interval, a discrete stochastic process model can be constructed. Next, letting the time interval shrink to zero, an Ito stochastic differential equation model for the dynamical system is obtained. This modeling procedure is thoroughly explained and illustrated for randomly varying systems in population biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation. Computer programs, given throughout the text, are useful in solving representative stochastic problems. Analytical and computational exercises are provided in each chapter that complement the material in the text. Modeling with Itô Stochastic Differential Equations is useful for researchers and graduate students. As a textbook for a graduate course, prerequisites include probability theory, differential equations, intermediate analysis, and some knowledge of scientific programming.

Mathematical Methods In Medical And Biological Sciences

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Author : Harendra Singh
language : en
Publisher: Elsevier
Release Date : 2024-11-05

Mathematical Methods In Medical And Biological Sciences written by Harendra Singh and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Mathematics categories.

Mathematical Methods in Medical and Biological Sciences presents mathematical methods for computational models arising in the medical and biological sciences. The book presents several real-life medical and biological models, such as infectious and non-infectious diseases that can be modeled mathematically to accomplish profound research in virtual environments when the cost of laboratory expenses is relatively high. It focuses on mathematical techniques that provide global solutions for models arising in medical and biological sciences by considering their long-term benefits. In addition, the book provides leading-edge developments and insights for a range of applications, including epidemiological modeling of pandemic dynamics, viral infection developments, cancer developments, blood oxygen dynamics, HIV infection spread, reaction-diffusion models, polio infection spread, and chaos modeling with fractional order derivatives. - Presents the mathematical treatment of a wide range of real-life medical and biological models, including both infectious and non-infectious diseases - Provides in-depth analysis of the spread of Covid-19, polio, and HIV, including discussion of computational methods and applications - Includes computational modeling methods, along with their practical applications, providing the basis for further exploration and research in epidemiology and applied biomedical sciences

Computer Literature Bibliography 1964 1967

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Author : W. W. Youden
language : en
Publisher:
Release Date : 1965

Computer Literature Bibliography 1964 1967 written by W. W. Youden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Computers categories.

Applied Stochastic Analysis

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Author : Weinan E
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-09-22

Applied Stochastic Analysis written by Weinan E and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-22 with Education categories.

This is a textbook for advanced undergraduate students and beginning graduate students in applied mathematics. It presents the basic mathematical foundations of stochastic analysis (probability theory and stochastic processes) as well as some important practical tools and applications (e.g., the connection with differential equations, numerical methods, path integrals, random fields, statistical physics, chemical kinetics, and rare events). The book strikes a nice balance between mathematical formalism and intuitive arguments, a style that is most suited for applied mathematicians. Readers can learn both the rigorous treatment of stochastic analysis as well as practical applications in modeling and simulation. Numerous exercises nicely supplement the main exposition.

Encyclopedia Of Bioinformatics And Computational Biology

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Author :
language : en
Publisher: Elsevier
Release Date : 2018-08-21

Encyclopedia Of Bioinformatics And Computational Biology written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-21 with Medical categories.

Encyclopedia of Bioinformatics and Computational Biology: ABC of Bioinformatics, Three Volume Set combines elements of computer science, information technology, mathematics, statistics and biotechnology, providing the methodology and in silico solutions to mine biological data and processes. The book covers Theory, Topics and Applications, with a special focus on Integrative –omics and Systems Biology. The theoretical, methodological underpinnings of BCB, including phylogeny are covered, as are more current areas of focus, such as translational bioinformatics, cheminformatics, and environmental informatics. Finally, Applications provide guidance for commonly asked questions. This major reference work spans basic and cutting-edge methodologies authored by leaders in the field, providing an invaluable resource for students, scientists, professionals in research institutes, and a broad swath of researchers in biotechnology and the biomedical and pharmaceutical industries. Brings together information from computer science, information technology, mathematics, statistics and biotechnology Written and reviewed by leading experts in the field, providing a unique and authoritative resource Focuses on the main theoretical and methodological concepts before expanding on specific topics and applications Includes interactive images, multimedia tools and crosslinking to further resources and databases