Approximating the solution of an SDE model for cancer cell growth with a PDE using the Feynman-Kac Theorem

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October 11, 2015
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In this work the Feynman-Kac theorem was used to derive a Partial Differential Equation (Kolmogorov Equation) from an SDE model for cancer cell growth.Two Numerical schemes specifically for Stochastic Differential Equations were used to solve for the time it takes for the cancerous cells to be extinct (Persistence Time) and the resulting deterministic PDE so derived was solved using the Finite Difference approach.Tabular and Graphical results are presented and discussed. The results obtained showed that the Stochastic Numerical schemes; the Euler Maruyama and the Milstein Method employed for the SDE gave fairly consistent results while the Finite difference method employed for the deterministic PDE gave a very close approximate results to that of the SDEs.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology In partial fulfillment of the requirement for the Degree of M.Phil in Applied Mathematics,