Mathematica 7 has limitations when it comes to solving nonlinear second-order partial differential equations (PDEs) directly using DSolve, often returning the original equation as output. While Mathematica can solve PDEs with known solutions, nonlinear equations typically require numerical methods. For effective use, it is recommended to start with a simple example that has a known closed-form solution to familiarize oneself with the syntax and capabilities of Mathematica. In the context of groundwater flow, the specific equation presented involves parameters such as storativity, recharge, and transmissivity. To solve this equation numerically, methods like Finite Element Method (FEM) or Finite Difference Method (FDM) can be employed. It is crucial to define initial and boundary conditions for accurate modeling in Mathematica, especially for a final year project focused on groundwater modeling.
