We discuss our preliminary results in building a configurable accelerator for differential equation time stepping and iterative methods for algebraic equations. Relative to prior efforts in building hardware accelerators for numerical methods, our focus is on the following: 1) Demonstrating a higher order of numerical convergence that is needed to actually support existing numerical algorithms. 2) Providing the capacity for wide vectors of variables by keeping the hardware design components as simple as possible. 3) Demonstrating configurable hardware support for a variety of numerical algorithms that form the core of scientific computation libraries. These efforts are toward the goal of making the accelerator democratically accessible by computational scientists.