This is the first book on the numerical method of lines, a relatively new method for solving partial differential equations. The Numerical Method of Lines is also the first book to accommodate all major classes of partial differential equations. This is essentially an applications book for computer scientists. The author will separately offer a disk of FORTRAN 77 programs with 250 specific applications, ranging from "Shuttle Launch Simulation" to "Temperature Control of a Nuclear Fuel Rod."

The Numerical Method of Lines: Integration of Partial Differential Equations

Computers & Technology

Schiesser, William E.

Software

Academic Press

This book presents a methodology for the development and computer implementation of dynamic models for transport process systems. Rather than developing the general equations of transport phenomena, it develops the equations required specifically for each new example application. These equations are generally of two types: ordinary differential equations (ODEs) and partial differential equations (PDEs) for which time is an independent variable. The computer-based methodology presented is general purpose and can be applied to most applications requiring the numerical integration of initial-value ODEs/PDEs. A set of approximately two hundred applications of ODEs and PDEs developed by the authors are listed in Appendix 8.

Dynamic Modeling of Transport Process Systems

Business & Money

Silebi, C. A.

Management & Leadership

ODE/PDE Alpha-Synuclein Models for Parkinson’s Disease discusses a mechanism for the evolution of Parkinson’s Disease (PD) based on the dynamics of the protein α-synuclein, a monomer that has been implicated in this disease. Specifically, α-synuclein morphs and aggregates into a polymer that can interfere with functioning neurons and lead to neurodegenerative pathology. This book first demonstrates computer-based implementation of a prototype ODE/PDE model for the dynamics of the α-synuclein monomer and polymer, and then details the methodology for the numerical integration of ODE/PDE systems which can be applied to computer-based analyses of alternative models based on the reader's interest. This book facilitates immediate computer use for research without the necessity to first learn the basic concepts of numerical analysis for ODE/PDEs and programming algorithms

ODE/PDE α-synuclein Models for Parkinson’s Disease

Health, Fitness & Dieting

Diseases & Physical Ailments

Numerical PDE Analysis of Retinal Neovascularization: Mathematical Model Computer Implementation in R

Science & Math

Biological Sciences

ODE/PDE Analysis of Antibiotic/Antimicrobial Resistance: Programming in R

Modeling of Post-Myocardial Infarction: ODE/PDE Analysis with R

PDE Modeling of Tissue Engineering and Regenerative Medicine: Computer Analysis in R presents the formulation and computer implementation of mathematical models for the forefront research areas of tissue engineering and regenerative medicine. The mathematical model discussed in this book consists of a system of eight partial differential equations (PDEs) with dependent variables. The computer-based example models are presented through routines coded 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. Includes detailed examples that the reader can execute on modest computers.

PDE Modeling of Tissue Engineering and Regenerative Medicine: Computer Analysis in R

A Compendium of Partial Differential Equation Models presents numerical methods and associated computer codes in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs), one of the mostly widely used forms of mathematics in science and engineering. The authors focus on the method of lines (MOL), a well-established numerical procedure for all major classes of PDEs in which the boundary value partial derivatives are approximated algebraically by finite differences. This reduces the PDEs to ordinary differential equations (ODEs) and thus makes the computer code easy to understand, implement, and modify. Also, the ODEs (via MOL) can be combined with any other ODEs that are part of the model (so that MOL naturally accommodates ODE/PDE models). This book uniquely includes a detailed line-by-line discussion of computer code as related to the associated equations of the PDE model.

A Compendium of Partial Differential Equation Models: Method of Lines Analysis with Matlab

Griffiths, Graham W.

Mathematics

Cambridge University Press

Aimed at graduates and researchers, and requiring only a basic knowledge of multi-variable calculus, this introduction to computer-based partial differential equation (PDE) modeling provides readers with the practical methods necessary to develop and use PDE mathematical models in biomedical engineering. Taking an applied approach, rather than using abstract mathematics, the reader is instructed through six biomedical example applications, each example characterized by step-by-step discussions of established numerical methods and implemented in reliable computer routines. Adopting this technique, the reader will understand how PDE models are formulated, implemented and tested. Supported by a set of rigorously tested general purpose PDE routines online, and with enhanced understanding through animations, this book will be ideal for anyone faced with interpreting large experimental data sets that need to be analyzed with PDE models in biomedical engineering.

Partial Differential Equation Analysis in Biomedical Engineering: Case Studies with Matlab

Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear partial differential equations. The author’s primary focus is on models expressed as systems of PDEs, which generally result from including spatial effects so that the PDE dependent variables are functions of both space and time, unlike ordinary differential equation (ODE) systems that pertain to time only. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes: <ul>
<li>R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for PDEs</li> <li>Models as systems of PDEs and associated initial and boundary conditions with explanations of the associated chemistry, physics, biology, and physiology</li> <li>Numerical solutions of the presented model equations with a discussion of the important features of the solutions</li> <li>Aspects of general PDE computation through various biomedical science and engineering applications</li> </ul>
Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.

Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R

wiley

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