Download or read book Time Delay ODE PDE Models written by W.E. Schiesser and published by CRC Press. This book was released on 2019-11-25 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Delay Differential Equations with Applications to the Life Sciences written by hal smith and published by Springer Science & Business Media. This book was released on 2010-09-29 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Delay Ordinary and Partial Differential Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2023-08-28 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides exact solutions Describes numerical methods or numerical solutions, analytical methods, stability/instability issues Focus on partial differential equations
Download or read book Computational Modeling Of The Covid 19 Disease Numerical Ode Analysis With R Programming written by William E Schiesser and published by World Scientific. This book was released on 2020-06-16 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Systems with Delays written by A. V. Kim and published by John Wiley & Sons. This book was released on 2015-07-23 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim of the book is to present new constructive methods of delay differential equation (DDE) theory and to give readers practical tools for analysis, control design and simulating of linear systems with delays. Referred to as “systems with delays” in this volume, this class of differential equations is also called delay differential equations (DDE), time-delay systems, hereditary systems, and functional differential equations. Delay differential equations are widely used for describing and modeling various processes and systems in different applied problems At present there are effective control and numerical methods and corresponding software for analysis and simulating different classes of ordinary differential equations (ODE) and partial differential equations (PDE). There are many applications for these types of equations, because of this progress, but there are not as many methodologies in systems with delays that are easily applicable for the engineer or applied mathematician. there are no methods of finding solutions in explicit forms, and there is an absence of generally available general-purpose software packages for simulating such systems. Systems with Delays fills this void and provides easily applicable methods for engineers, mathematicians, and scientists to work with delay differential equations in their operations and research.
Download or read book Handbook of Exact Solutions to Mathematical Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2024-08-26 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Solving Differential Equations in R written by Karline Soetaert and published by Springer Science & Business Media. This book was released on 2012-06-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advanced Analytic and Control Techniques for Thermal Systems with Heat Exchangers written by Libor Pekar and published by Academic Press. This book was released on 2020-07-10 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Mathematical Modeling and Applications in Nonlinear Dynamics written by Albert C.J. Luo and published by Springer. This book was released on 2016-01-28 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.
Download or read book Separation of Variables and Exact Solutions to Nonlinear PDEs written by Andrei D. Polyanin and published by CRC Press. This book was released on 2021-09-20 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Separation of Variables and Exact Solutions to Nonlinear PDEs is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear partial differential equations (PDEs). It also presents the direct method of symmetry reductions and its more general version. In addition, the authors describe the differential constraint method, which generalizes many other exact methods. The presentation involves numerous examples of utilizing the methods to find exact solutions to specific nonlinear equations of mathematical physics. The equations of heat and mass transfer, wave theory, hydrodynamics, nonlinear optics, combustion theory, chemical technology, biology, and other disciplines are studied. Particular attention is paid to nonlinear equations of a reasonably general form that depend on one or several arbitrary functions. Such equations are the most difficult to analyze. Their exact solutions are of significant practical interest, as they are suitable to assess the accuracy of various approximate analytical and numerical methods. The book contains new material previously unpublished in monographs. It is intended for a broad audience of scientists, engineers, instructors, and students specializing in applied and computational mathematics, theoretical physics, mechanics, control theory, chemical engineering science, and other disciplines. Individual sections of the book and examples are suitable for lecture courses on partial differential equations, equations of mathematical physics, and methods of mathematical physics, for delivering special courses and for practical training.
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Download or read book Extremum Seeking Through Delays and PDEs written by Tiago Roux Oliveira and published by SIAM. This book was released on 2022-12-05 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extremum Seeking through Delays and PDEs, the first book on the topic, expands the scope of applicability of the extremum seeking method, from static and finite-dimensional systems to infinite-dimensional systems. Readers will find numerous algorithms for model-free real-time optimization are developed and their convergence guaranteed, extensions from single-player optimization to noncooperative games, under delays and PDEs, are provided, the delays and PDEs are compensated in the control designs using the PDE backstepping approach, and stability is ensured using infinite-dimensional versions of averaging theory, and accessible and powerful tools for analysis. This book is intended for control engineers in all disciplines (electrical, mechanical, aerospace, chemical), mathematicians, physicists, biologists, and economists. It is appropriate for graduate students, researchers, and industrial users.
Download or read book Proceedings of 2021 5th Chinese Conference on Swarm Intelligence and Cooperative Control written by Zhang Ren and published by Springer Nature. This book was released on 2022-07-29 with total page 1902 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book European Control Conference 1995 written by and published by European Control Association. This book was released on 1995-09-05 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the European Control Conference 1995, Rome, Italy 5-8 September 1995
Download or read book Stability of Linear Delay Differential Equations written by Dimitri Breda and published by Springer. This book was released on 2014-10-21 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra. The purpose of the book is to provide a complete and self-contained treatment, which includes the basic underlying mathematics and numerics, examples from population dynamics and engineering applications, and Matlab programs implementing the proposed numerical methods. A number of proofs is given to furnish a solid foundation, but the emphasis is on the (unifying) idea of the pseudospectral technique for the stability analysis of DDEs. It is aimed at advanced students and researchers in applied mathematics, in dynamical systems and in various fields of science and engineering, concerned with delay systems. A relevant feature of the book is that it also provides the Matlab codes to encourage the readers to experience the practical aspects. They could use the codes to test the theory and to analyze the performances of the methods on the given examples. Moreover, they could easily modify them to tackle the numerical stability analysis of their own delay models.
Download or read book Applications of Dynamical Systems in Biology and Medicine written by Trachette Jackson and published by Springer. This book was released on 2015-07-06 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Membrane Transport and Renal Physiology written by Harold E. Layton and published by Springer Science & Business Media. This book was released on 2002-08-06 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
