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 reprodu. �Read more...
Abstract:
With a step-by-step approach to solving partial differential equations (PDEs), this book successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. It is suitable for graduate-level courses in mathematics, biology, and engineering. �Read more...
Author(s): William E. Schiesser
Edition: 1
Publisher: Wiley
Year: 2014
Language: English
Pages: 344
City: Hoboken
Tags: Библиотека;Компьютерная литература;R;
Content: Cover
Title Page
Contents
Preface
Chapter 1 Introduction to Partial Differentiation Equation Analysis: Chemotaxis
1.1 Introduction
1.2 Linear Diffusion Model
1.3 Nonlinear Chemotaxis Model
1.4 Method of Lines Solution of 2-PDE Chemotaxis Model
1.4.1 Main Program
1.4.2 ODE Routine
1.5 Model Output
1.6 Computation of PDE Terms
1.7 Conclusions
References
Chapter 2 Pattern Formation
2.1 Introduction
2.2 Two PDE Model
2.2.1 ODE Routine
2.2.2 Main Program
2.2.3 Numerical Solution
2.3 Three PDE Model
2.3.1 ODE Routine
2.3.2 Main Program
2.3.3 Supplemental Routine. 2.3.4 Numerical Solution2.4 Conclusions
References
Chapter 3 Belousov-Zhabotinskii Reaction System
3.1 Introduction
3.2 The Belousov-Zhabotinskii Reaction System
3.2.1 ODE Routine
3.2.2 Main Program
3.2.3 Model Output
3.3 Conclusions
Reference
Chapter 4 Hodgkin-Huxley and Fitzhugh-Nagumo Models
4.1 Introduction
4.2 PDE Model
4.3 MOL Routines
4.3.1 ODE Routine
4.3.2 Main Program
4.4 Model Output
4.5 Discontinuous Initial Condition
4.6 Conclusions
References
Chapter 5 Anesthesia Spatiotemporal Distribution
5.1 Introduction
5.2 Two PDE Model
5.2.1 Main Program. 5.2.2 ODE Routine5.2.3 Other PDE Routines
5.2.4 Model Output
5.3 Conclusions
5.4 Model Extension
5.4.1 ODE Routine for the Extended Model
5.4.2 Main Program for the Extended Model
5.4.3 Output for the Extended Model
Acknowledgment
References
Chapter 6 Influenza with Vaccination and Diffusion
6.1 Introduction
6.2 Five PDE Model
6.2.1 ODE Routine
6.2.2 Main Program
6.2.3 Model Output
6.3 Summary
References
Chapter 7 Drug Release Tracking
7.1 Introduction
7.2 Three PDE Model
7.2.1 ODE Routine
7.2.2 Rate Functions
7.2.3 Main Program
7.3 Model Output
7.3.1 Base Case. 7.3.2 Variation of Spatial Differentiation7.3.3 Variation of Polymer Stress
7.4 Alternate Coordinate Systems
7.5 Summary
References
Chapter 8 Temperature Distributions in Cryosurgery
8.1 Introduction
8.2 PDE Model
8.3 Method of Lines Analysis
8.3.1 ODE Routine
8.3.2 Physical Property Routines
8.3.3 Main Program
8.4 Numerical Output
8.5 Variations in the Model
8.6 Summary
References
Index.
