Numerically solving partial differential equations (PDE) has made a significant impact on science and engineering since the last century. The finite difference method and finite elements method are two main methods for numerical PDEs. This talk presents a new method that uses gradually varied functions to solve partial differential equations, specifically in groundwater flow equations. We first introduce basic partial differential equations including elliptic, parabolic, and hyperbolic differential equations and the brief descriptions of their numerical solving methods. Second, we establish a mathematical model based on gradually varied functions for parabolic differential equations, then we use this method for groundwater data reconstruction. This model can also be used to solve elliptic differential equations. Lastly, we present a case study for solving hyperbolic differential equations using our new method.