The objective of the proposed research is the investigation and the implementation of partial differential equation solvers using analog VLSI circuits, specifically the design, fabrication and evaluation of a programmable analog laplace equation solvers. The main advantages of the proposed approach include speed improvement, robustness and fault tolerance. This research demonstrates the feasibility of analog VLSI partial differential equation solvers. It will have an impact on engineering disciplines where a real time solution of these types of equations are required.