WELL-POSEDNESS AND CONVERGENCE ANALYSIS OF THE MULTI-LEVEL MONTE CARLO METHOD FOR A SYSTEM OF PDEs WITH RANDOM COEFFICIENTS MODELING DRUG TRANSPORT IN TUMORS

In this paper, we consider a mathematical model of drug transport in tumors given by a system of PDEs with random coefficients and initial data. The existence of a strong solution to this model in any dimension is proved under the assumption that the random coefficients are uniformly bounded. Along with the finite difference method (FD), we applied a multilevel Monte Carlo method to simulate these random PDEs. We also derived the overall convergence rate and estimated the total computation cost. Finally, some numerical results are presented to confirm our theoretical results. Additionally, we provide a comparison between the stochastic and deterministic approaches for solving the drug transport equation, demonstrating the efficiency of the method we adopted.