Efficient numerical solution of the brain glioblastomas proliferation-invasion model

Brain Glioblastomas are considered one of the most aggressive brain tumours due to their rapid proliferation and infiltration of the brain tissue. Therefore, the efficient solution of mathematical models of this disease may improve understanding of its dynamics. In this work, we numerically solve the Partial Differential Equation modelling the proliferation-invasion of brain glioblastomas. We apply the Crank-Nicolson method to obtain the associated algebraic system of equations of the model and compare computation times for LU-decomposition, Gauss-Seidel, and Conjugate Gradient methods. These results suggest that solution times may be reduced by exploiting the underlying structure of the derived system of algebraic equations.