Quantifying uncertainty of a mathematical model of drug transport in tumors

Abstract

This paper presents a numerical simulation in the two-dimensional for a system of PDE governing drug transport in tumors with random coefficients, which is described as a random field. The continuous stochastic field is approximated by a finite number of random variables via the Karhunen–Loève expansion and transform the stochastic problem into a determinate one with a parameter in high dimension. Then we apply a finite difference scheme and the Euler–Maruyama Integrator in time. The Monte Carlo method is used to compute corresponding simple averages. We compute the error estimate using the Central Limits Theorem (CLT) and the error estimate for the finite difference method. Some numerical results are simulated to illustrate the theoretical analysis. We also propose a comparison between the stochastic and determinate solving processes of our system where we show the efficiency of our adopted method.