A method that replaces the temporal partial differential operators ∂n/∂tn of a partial differential equation (PDE) with Laplace domain impedances sn is proposed for realizing analog circuits that solve the wave equation. A systolic array of analog circuit modules is employed to simulate electromagnetic wave propagation. Mathematical models and corresponding analog circuits are described for internal and boundary modules in the systolic array. Dirichlet, Neumann, and radiation boundary conditions are considered. The system is simulated using ideal circuits in Cadence Spectre. Signal flow graphs and transfer functions for 1-D wave equation solvers are obtained. Errors associated with the analog wave equation solver is quantified by comparing the results with a MATLAB based finite difference time domain simulation. Finally, the case where multiple medium boundaries is present is analyzed.