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The Numerical Method of Lines
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."
A Compendium of Partial Differential Equation Models
Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.
Traveling Wave Analysis of Partial Differential Equations
Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problems that can be used to evaluate numerical methods. This book survey...
Dynamic Modeling of Transport Process Systems
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.
Computational Modeling Of The Covid-19 Disease: Numerical Ode Analysis With R Programming
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.
Partial Differential Equation Analysis in Biomedical Engineering
Gives graduate students and researchers an introductory overview of partial differential equation analysis of biomedical engineering systems through detailed examples.
Traveling Wave Analysis of Partial Differential Equations
Partial Differential Equations have been developed and used in science and engineering for more than 200 years, yet they remain a very active area of research, both because of their role in mathematics and their application to virtually all areas of science and engineering. This research is due relatively recently to the development of computer solution methods for PDEs that have extended PDE applications in quantifying board areas of physical, chemical, and biological phenomena. This book surveys some of these new development in analytical and numerical method, and relates the two through a series of PDF examples. The PDFs that have been selected are largely, "named" in thee sense that they have the names of their original contributors. These names usually reflect that the PDFs are widely recognized and used in many application areas. The development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problem that can be used to evaluate numerical methods.
Moving Boundary Pde Analysis
The book is directed to the numerical integration (solution) of systems of partial differential equations (PDEs) for which the boundary conditions move in space. In applications, the physical boundaries move as the solution evolves in time. The book provides examples of the applications in tumor growth and atherosclerosis
Computational Mathematics in Engineering and Applied Science
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
Spline Collocation Methods for Partial Differential Equations
A comprehensive approach to numerical partial differential equations Spline Collocation Methods for Partial Differential Equations combines the collocation analysis of partial differential equations (PDEs) with the method of lines (MOL) in order to simplify the solution process. Using a series of example applications, the author delineates the main features of the approach in detail, including an established mathematical framework. The book also clearly demonstrates that spline collocation can offer a comprehensive method for numerical integration of PDEs when it is used with the MOL in which spatial (boundary value) derivatives are approximated with splines, including the boundary condition...
