Abstract

We consider a tumor growth model initially proposed by Ward and King in 1997. Our primary goal is to find an efficient and accurate numerical method for the identification of parameters in the model (an inverse problem) from measurements of the evolving tumor over time. The so-called direct problem, in this case, is to solve a system of coupled nonlinear partial differential equations for given fixed values of the unknown parameters. We compare several derivative-free and gradient-based methods for the solution of the inverse problem which is formulated as an optimization problem with the system of partial differential equations (PDEs) as the constraint. We modify the original model by incorporating uncertainty in one of the parameters. We use the Monte Carlo method based sampling strategy, coupled with optimization methods, for the uncertainty quantification.

Library of Congress Subject Headings

Tumors--Growth--Mathematical models; Differential equations, Partial--Numerical solutions; Mathematical optimization

Publication Date

7-25-2018

Document Type

Thesis

Student Type

Graduate

Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)

Advisor

Baasansuren Jadamba

Advisor/Committee Member

Akhtar Khan

Advisor/Committee Member

Ephraim Agyingi

Campus

RIT – Main Campus

Plan Codes

ACMTH-MS

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