| Summary: | Philosophiae Doctor - PhD === Cancer is a complex disease that involves a sequence of gene-environment interactions
in a progressive process that cannot occur without dysfunction in multiple systems.
From a mathematical point of view, the sequence of gene-environment interactions often
leads to mathematical models which are hard to solve analytically. Therefore, this
thesis focuses on the design and implementation of reliable numerical methods for nonlinear,
first order delay differential equations, second order non-linear time-dependent
parabolic partial (integro) differential problems and optimal control problems arising
in cancer modeling. The development of cancer modeling is necessitated by the lack of
reliable numerical methods, to solve the models arising in the dynamics of this dreadful
disease. Our focus is on chemotherapy, biological stoichometry, double infections,
micro-environment, vascular and angiogenic signalling dynamics. Therefore, because
the existing standard numerical methods fail to capture the solution due to the behaviors
of the underlying dynamics. Analysis of the qualitative features of the models with
mathematical tools gives clear qualitative descriptions of the dynamics of models which
gives a deeper insight of the problems. Hence, enabling us to derive robust numerical
methods to solve such models. === 2021-04-30
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