Numerical analysis of a mathematical model of multiphase tissue growth

Asgir, Maryam (2015) Numerical analysis of a mathematical model of multiphase tissue growth. Masters thesis (MPhil), University of Sussex.

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Abstract

In this thesis we study a mathematical system of equations that models multi phase tissue
growth. The mathematical system comprises of three coupled equations: an advection diffusion
equation for a scalar quantity that defines the volume fraction of one cell type and two
constitutive relations for the pressure field and volume averaged velocity field.
A numerical discretisation of this mathematical model is derived using a coupled finite volume
- finite difference scheme. Stability bounds on the approximate solution of a simplified version
of the model are proved together with a convergence results relating the approximate solution
to the weak solution of the simplified model.
In addition an efficient and reliable numerical scheme is implemented in the Matlab programming
language to solve the numerical approximation of the full model and computational results
are presented.

Item Type: Thesis (Masters)
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Library Cataloguing
Date Deposited: 03 Jun 2015 05:43
Last Modified: 07 Jul 2017 05:59
URI: http://srodev.sussex.ac.uk/id/eprint/53796

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