June 13, 2019 Forthcoming
Reference - 128 Pages - 86 B/W Illustrations
ISBN 9780367224837 - CAT# K421635
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Mathematical models stated as systems of partial di
erential equations (PDEs) are
broadly used in biology, chemistry, physics and medicine (physiology). These models
describe the spatial and temporial variations of the problem system dependent variables,
such as temperature, chemical and biochemical concentrations and cell densities, as a
function of space and time (spatiotemporal distributions).
For a complete PDE model, initial conditions (ICs) specifying how the problem system
starts and boundary conditions (BCs) specifying how the system is de ned at its spatial
boundaries, must also be included for a well-posed PDE model.
In this book, PDE models are considered for which the physical boundaries move with
time. For example, as a tumor grows, its boundary moves outward. In atherosclerosis,
the plaque formation on the arterial wall moves inward, thereby restricting blood ow
with serious consequences such as stroke and myocardial infarction (heart attack).
These two examples are considered as applications of the reported moving boundary
PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of
documented routines coded in R, a quality, open-source scienti c programming system.
The routines are provided as a download so that the teacher/analyst/researcher can
use MFPDE models without having to rst study numerical methods and computer
1. PDE Model Formulation. 2. PDE Model Implementation. 3. PDE Model Output. 4. Tumor growth. 5. Plaque Formation in Atherosclerosis. Appendix A1. Test of Spline Regridding. Appendix A2. Test of Moving Boundary Algorithm Spline Formulation. Appendix A3. Test of Moving Boundary Algorithm Finite Difference Formulation.