The simulation language TKSL and modern Taylor series method has proved to be very powerful computing tools for extremely exact, stable and fast numerical solutions of systems of differential equations. In a natural way, TKSL also involves solutions of problems that can be reduced to solving a system of differential equations. It is known that the Taylor series method is a parallel one and therefore attempts at a parallel interpretation in a suitable hardware can be expected. We outline the design and implementation of an FPGA-based numerical integrator that will form the basis of our FPGA-based parallel hardware. Currently, our processor uses the Taylor series numerical integration algorithm to solve the ordinary differential equations. A numerical integrator simulator is used for simulation of a behavior of Taylor series numerical integrator.