New computational modeling for solving higher order ODE based on FPGA

Abstract

In this paper we propose a method for solving complex higher order ordinary differential equations (ODE) based on an emulation of the analog computing paradigm on digital hardware platforms. In this case, we mimic real analog system elements by digital discretized models. Due to the flexibility and reconfigurability of FPGA and also the possibility of system behavioral modeling through hardware description languages (HDL), we are able to create all fundamental elements that are necessary to both simulating complex systems and the modeling of any ordinary differential equations (ODE) or a system simulation based on ODEs. We therefore propose a novel methodology of solving systems and higher order ODEs. This technique is similar to the analog computing but with the key difference that we possess more flexibility and are able to control at will the precision level wanted/needed. Further features are values scaling of both the results and internal variables.