Numerical method for ɛ-optimal approximation of tumor growth inhibition by GM-CSF treatment

In this thesis we construct a computational method for ɛ-optimized approximation inhibition of tumor growth using GM-CSF treatment. First of all, we formulate and solve the system of partial differential equations. It’s a free boundary model, all equations contain nonlinear components as well as first, second and even third order partial derivatives. In order to solve such a complicated system of equations, we create our own numerical method to find optimal control of inhibiting tumor growth by GM-CSF using the finite element method implemented in the FreeFem ++ package.
Furthermore, we construct dual dynamic programming approach to formulate sufficient ɛ-optimality condition of the treatment and next we calculate numerically ɛ-optimal treatment.
Finally we are able to verify the dissertation thesis positively, i.e. confirmation that it is possible to calculate the ɛ-optimal dosage of GM-CSF, resulting in inhibition of tumor growth