International Journal of Control, Vol.92, No.11, 2712-2736, 2019
Numerical solution of optimal control problem for a model of tumour growth with drug application
In this study, a combination of spectral and fixed point methods is used to solve an optimal control problem for a model of tumour growth. The growth of tumour is modelled using three first-order hyperbolic equations describing the evolution of cells and two second-order parabolic equations describing the diffusion of nutrient and drug concentration. In the optimal control problem, four control variables are employed to control the concentration of nutrient and drug on the boundary and inside the tumour. Since the problem is nonlinear, applying the fixed point method, in each step of iteration, the problem is changed to a linear one and the parabolic equations are solved using the spectral method. The convergence and stability of method are proven. Some examples are considered to illustrate the efficiency of method. Finally, some figures are provided to reflect the effects of control on the densities of tumourcells.