Author: W.E. Schiesser
Publisher: CRC Press
ISBN: 1000763730
Category : Medical
Languages : en
Pages : 276
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Book Description
Time delayed (lagged) variables are an inherent feature of biological/physiological systems. For example, infection from a disease may at first be asymptomatic, and only after a delay is the infection apparent so that treatment can begin. Thus, to adequately describe physiological systems, time delays are frequently required and must be included in the equations of mathematical models. 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). The DODE/DPDE methodology is presented through a series of example applications, particularly in biomedical science and engineering (BMSE). The computer-based implementation of the example models is explained with routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, for example, no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The DPDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The example applications can first be executed to confirm the reported solutions, then extended by variation of the parameters and the equation terms, and even the formulation and use of alternative DODE/DPDE models.
Author: W.E. Schiesser
Publisher: CRC Press
ISBN: 1000763617
Category : Mathematics
Languages : en
Pages : 251
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Book Description
Time delayed (lagged) variables are an inherent feature of biological/physiological systems. For example, infection from a disease may at first be asymptomatic, and only after a delay is the infection apparent so that treatment can begin.Thus, to adequately describe physiological systems, time delays are frequently required and must be included in the equations of mathematical models. 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). The DODE/DPDE methodology is presented through a series of example applications, particularly in biomedical science and engineering (BMSE). The computer-based implementation of the example models is explained with routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The DPDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The example applications can first be executed to confirm the reported solutions, then extended by variation of the parameters and the equation terms, and even the forumulation and use of alternative DODE/DPDE models. • Introduces time delay ordinary and partial differential equations (DODE/DPDEs) and their numerical computer-based integration (solution) • Illustrates the computer implementation of DODE/DPDE models with coding (programming) in R, a quality, open-source scientific programming system readily available from the Internet • Applies DODE/DPDE models to biological/physiological systems through a series of examples • Provides the R routines for all of the illustrative applications through a download link • Facilitates the use of the models with reasonable time and effort on modest computers
Author: Andrei D. Polyanin
Publisher: CRC Press
ISBN: 1000925897
Category : Mathematics
Languages : en
Pages : 434
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Book Description
Provides exact solutions Describes numerical methods or numerical solutions, analytical methods, stability/instability issues Focus on partial differential equations
Author: William E Schiesser
Publisher: World Scientific
ISBN: 9811222894
Category : Medical
Languages : en
Pages : 109
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Book Description
The book is intended for readers who are interested in learning about the use of computer-based modelling of the COVID-19 disease. It provides a basic introduction to a five-ordinary differential equation (ODE) model by providing a complete statement of the model, including a detailed discussion of the ODEs, initial conditions and parameters, followed by a line-by-line explanation of a set of R routines (R is a quality, scientific programming system readily available from the Internet). The reader can access and execute these routines without having to first study numerical algorithms and computer coding (programming) and can perform numerical experimentation with the model on modest computers.
Author: Andrei D. Polyanin
Publisher: CRC Press
ISBN: 1040092934
Category : Mathematics
Languages : en
Pages : 660
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Book Description
This reference book describes the exact solutions of the following types of mathematical equations: ● Algebraic and Transcendental Equations ● Ordinary Differential Equations ● Systems of Ordinary Differential Equations ● First-Order Partial Differential Equations ● Linear Equations and Problems of Mathematical Physics ● Nonlinear Equations of Mathematical Physics ● Systems of Partial Differential Equations ● Integral Equations ● Difference and Functional Equations ● Ordinary Functional Differential Equations ● Partial Functional Differential Equations The book delves into equations that find practical applications in a wide array of natural and engineering sciences, including the theory of heat and mass transfer, wave theory, hydrodynamics, gas dynamics, combustion theory, elasticity theory, general mechanics, theoretical physics, nonlinear optics, biology, chemical engineering sciences, ecology, and more. Most of these equations are of a reasonably general form and dependent on free parameters or arbitrary functions. The Handbook of Exact Solutions to Mathematical Equations generally has no analogs in world literature and contains a vast amount of new material. The exact solutions given in the book, being rigorous mathematical standards, can be used as test problems to assess the accuracy and verify the adequacy of various numerical and approximate analytical methods for solving mathematical equations, as well as to check and compare the effectiveness of exact analytical methods.
Author: hal smith
Publisher: Springer Science & Business Media
ISBN: 1441976469
Category : Mathematics
Languages : en
Pages : 178
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Book Description
This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a reasonable background in ordinary differential equations and who would like to get to the applications quickly. The author has used preliminary notes in teaching such a course at Arizona State University over the past two years. This book focuses on the key tools necessary to understand the applications literature involving delay equations and to construct and analyze mathematical models involving delay differential equations. The book begins with a survey of mathematical models involving delay equations.
Author: Zhang Ren
Publisher: Springer Nature
ISBN: 9811939985
Category : Technology & Engineering
Languages : en
Pages : 1902
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Book Description
This book includes original, peer-reviewed research papers from the 2021 5th Chinese Conference on Swarm Intelligence and Cooperative Control (CCSICC2021), held in Shenzhen, China on January 19-22, 2022. The topics covered include but are not limited to: reviews and discussions of swarm intelligence, basic theories on swarm intelligence, swarm communication and networking, swarm perception, awareness and location, swarm decision and planning, cooperative control, cooperative guidance, swarm simulation and assessment. The papers showcased here share the latest findings on theories, algorithms and applications in swarm intelligence and cooperative control, making the book a valuable asset for researchers, engineers, and university students alike.
Author: Karline Soetaert
Publisher: Springer Science & Business Media
ISBN: 3642280706
Category : Computers
Languages : en
Pages : 258
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Book Description
Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.
Author: Harold E. Layton
Publisher: Springer Science & Business Media
ISBN: 9780387954813
Category : Mathematics
Languages : en
Pages : 438
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Book Description
The papers in this volume arose out of the workshop Membrane Transport and Renal Physiology, which was conducted as part of the IMA 1998-1999 program year, Mathematics in Biology. The workshop brought together physiologists, biophysicists, and applied mathematicians who share a common interest in solute and water transport in biological systems, especially in the integrated function of the kidney. Solute and water transport through cells involves fluxes across two cell membranes, usually via specialized proteins that are integral membrane components. By means of mathematical representations, transport fluxes can be related to transmembrane solute concentrations and electrochemical driving forces. At the next level of functional integration, these representations can serve as key components for models of renal transcellular transport. Ultimately, simulations can be developed for transport-dependent aspects of overall renal function. Workshop topics included solute fluxes through ion channels, cotransporters, and metabolically-driven ion pumps; transport across fiber-matrix and capillary membranes; coordinated transport by renal epithelia; the urine concetrating mechanism; and intra-renal hemodynamic control. This volume will be of interest to biological and mathematical scientists who would like a view of recent mathematical efforts to represent membrane transport and its role in renal function.
Author: Libor Pekar
Publisher: Academic Press
ISBN: 0128194235
Category : Technology & Engineering
Languages : en
Pages : 522
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Book Description
Advanced Analytic Control Techniques for Thermal Systems with Heat Exchangers presents the latest research on sophisticated analytic and control techniques specific for Heat Exchangers (HXs) and heat Exchanger Networks (HXNs), such as Stability Analysis, Efficiency of HXs, Fouling Effect, Delay Phenomenon, Robust Control, Algebraic Control, Geometric Control, Optimal Control, Fuzzy Control and Artificial Intelligence techniques. Editor Libor Pekar and his team of global expert contributors combine their knowledge and experience of investigated and applied systems and processes in this thorough review of the most advanced networks, analyzing their dynamics, efficiency, transient features, physical properties, performance, feasibility, flexibility and controllability. The structural and dynamic analyses and control approaches of HXNs, as well as energy efficient manipulation techniques are discussed, in addition to the design of the control systems through the full life cycle. This equips the reader with an understanding of the relevant theory in a variety of settings and scenarios and the confidence to apply that knowledge to solve problems in an academic or professional setting.Graduate students and early-mid career professionals require a robust understanding of how to suitably design thermal systems with HXs and HXNs to achieve required performance levels, which this book offers in one consolidated reference. All examples and solved problems included have been tried and tested, and these combined with the research driven theory provides professionals, researchers and students with the most recent techniques to maximize the energy efficiency and sustainability of existing and new thermal power systems. - Analyses several advanced techniques, the theoretical background of these techniques and includes models, examples and results throughout - Focusses on advanced analytic and control techniques which have been investigated or applied to thermal systems with HXs and HXNs - Includes practical applications and advanced ideas from leading experts in the field, as well as case studies and tested problems and solutions
