We tackle the important problem class of solving nonlinear partial differential equations. While nonlinear PDEs are typically solved in high-performance supercomputers, they are increasingly used in graphics and embedded systems, where efficiency is important. We use a hybrid analog-digital computer architecture to solve nonlinear PDEs that draws on the strengths of each model of computation and avoids their weaknesses. A weakness of digital methods for solving nonlinear PDEs is they may not converge unless a good initial guess is used to seed the solution. A weakness of analog is it cannot produce high accuracy results. In our hybrid method we seed the digital solver with a high-quality guess from the analog side. With a physically prototyped analog accelerator, we use this hybrid analog-digital method to solve the two-dimensional viscous Burgers' equation -an important and representative PDE. For large grid sizes and nonlinear problem parameters, the hybrid method reduces the solution time by 5.7×, and reduces energy consumption by 11.6×, compared to a baseline solver running on a GPU.