Chemotaxis Modeling of Autoimmune Inflammation. PDE Computer Analysis in R

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Cover Half Title Title Page Copyright Page Contents Preface Chapter 1: PDE Chemotaxis Model Formulation 1.1. Introduction 1.2. Three PDE model coordinatefree 1.3. Three PDE model formulation in spherical coordinates Summary and conclusion References Chapter 2: PDE Chemotaxis Model Implementation 2.1. Introduction 2.2. Coding of the chemotaxis model 2.2.1. Main program 2.2.2. ODE/MOL routine 2.2.3. Numerical, graphical output Summary and conclusion References Chapter 3: Analysis of the Chemotaxis Model Time Derivatives 3.1. Introduction 3.2. Analysis of the chemotaxis model time derivatives 3.2.1. Main program 3.2.2. ODE/MOL routine 3.2.3. Numerical, graphical output Summary and conclusion References Chapter 4: Analysis of the Chemotaxis PDE Model Terms 4.1. Introduction 4.2. R routines for PDE RHS, LHS terms 4.2.1. Main program 4.2.2. ODE/MOL routine 4.2.3. Numerical, graphical output Summary and conclusion References Chapter 5: Sensitivity Analysis of the Chemotaxis PDE Model Parameters 5.1. Introduction 5.2. R routines for Case 1 5.3. R routines for Case 2 5.4. R routines for Case 3 Summary and conclusion References Chapter 6: Extensions of the Three PDE Chemotaxis Model 6.1. Introduction 6.2. PDE chemotaxis model with anti-inflammatory drug 6.2.1. Main program 6.2.2. MOL/ODE routine 6.2.3. Numerical, graphical output 6.3. Multicomponent extension of PDE chemotaxis model 6.3.1. Main program 6.3.2. ODE/MOL routine 6.3.3. Numerical, graphical output Summary and conclusion References Appendix A1: Functions dss004, dss044 A1.1. dss004 listing A1.2. dss044 listing Appendix A2: Accuracy of Numerical PDE Solutions A2.1. h refinement A2.2. p refinement Index