Time delayed (lagged) variables are an inherent feature of biological/physiological systems.&nbsp; 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&nbsp;ordinary differential equations (DODEs) and partial differential equations (DPDEs).&nbsp; 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.&nbsp; Formal mathematics is minimized, e.g., no theorems and proofs.&nbsp;Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on&nbsp;modest computers. The DPDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences.&nbsp; 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

Time Delay ODE/PDE Models

Science & Math

Schiesser, W.E.

Biological Sciences

CRC-Press

Computational Transport Phenomena: Numerical Methods for the Solution of Transport Problems

Computational techniques have become indispensable tools in solving complex problems in transport phenomena. This book provides a clear, user-oriented introduction to the subject of computational transport phenomena. Each self-contained chapter includes a detailed worked example and a discussion of the problem system equations. Also included are the numerical methods used; computer code for the solution of the problem system equations; discussion of the numerical solution with emphasis on physical interpretation; and, when appropriate, a comparison of the numerical solution with an analytical solution or a discussion of how the numerical solution goes beyond what can be done analytically, especially for nonlinear problems. Intended for students and a broad range of scientists and engineers, the book includes computer code written in transportable Fortran so the reader can produce the numerical solutions and then extend them to other cases.

Silebi, C. A.

Mathematics

Cambridge University Press

Physics

Computational Mathematics in Engineering and Applied Science provides numerical algorithms and associated software for solving a spectrum of problems in ordinary differential equations (ODEs), differential algebraic equations (DAEs), and partial differential equations (PDEs) that occur in science and engineering. It presents detailed examples, each including a complete analysis of a computer code written in transportable Fortran 77. Each example also includes a discussion of the problem equations, the coding of the equations, and the computed numerical solution. The benefits of using quality general-purpose library routines to solve ODE/DAE/PDE problems are illustrated as well. This popular, classic book is a valuable reference for methodologies in numerical mathematics applicable to a broad spectrum of problems encountered across many disciplines- virtually all fields of science and engineering. It also serves as an excellent text for senior undergraduates or beginning graduate students in computational science.

Computational Mathematics in Engineering and Applied Science: ODEs, DAEs, and PDEs (Symbolic & Numeric Computation)

Computers & Technology

Computer Science

Time Delay ODE/PDE Models: Applications in Biomedical Science and Engineering

This book provides a set of ODE/PDE integration routines in the six most widely used computer languages, enabling scientists and engineers to apply ODE/PDE analysis toward solving complex problems. This text concisely reviews integration algorithms, then analyzes the widely used Runge-Kutta method. It first presents a complete code before discussing its components in detail, focusing on integration concepts such as error monitoring and control. The format allows scientists and engineers to understand the basics of ODE/PDE integration, then calculate sample numerical solutions within their targeted programming language. The applications discussed can be used as templates for the development of a spectrum of new applications.

Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple, and MATLAB

Lee, H.J.

Chapman and Hall/CRC

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