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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Robust numerical methods to solve differential equations arising in cancer modeling

Shikongo, Albert January 2020 (has links)
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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