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Moving Boundary PDE Analysis - Biomedical Applications in R (Hardcover)
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Moving Boundary PDE Analysis - Biomedical Applications in R (Hardcover)
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Mathematical models stated as systems of partial differential
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 defined 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 flow 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 scientific programming
system. The routines are provided as a download so that the
reader/analyst/researcher can use MFPDE models without having to
first study numerical methods and computer programming.
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