Currently, a person diagnosed with glioblastoma (GBM), a highly invasive cancer of the structural cells in the brain, has an extremely low chance of long-term survival. One of the obstacles in treating GBM is the inability of current medical imaging technology to observe growth at an extremely small scale. Our task, in cooperation with IBM Corporation and researchers at Harvard University, is to develop a continuum model that accounts for both the proliferation and migration of tumor cells. In formulating this model, we will use a system of partial differential equations to describe the dynamics of the tumor and its effects on the surrounding brain tissue. In addition, we will employ finite difference methods to approximate the solution to the system. Our goal is to utilize our model in understanding patterns and initial stages of tumor growth.