RHCOS: An Area-efficient Reconfigurable High-precision Solver for Complex Ordinary Differential Equations

Abstract

Complex ordinary differential equations (ODEs) are vital for scientific computations. This paper presents a Reconfigurable High-precision Complex ODE Solver (RHCOS) on FPGA with high area-efficiency. The RHCOS efficiently integrates Runge-Kutta and Adams algorithm by reconstructing the recursive structures through unified computing units and dynamic coefficient switching. Additionally, a cyclic update cache mechanism is introduced to reduce memory accesses and latency. Experimental results show that, for solving six-degree-of-freedom spatial dynamics equations, the RHCOS achieves a 14.1× speedup over software solution at 200 MHz, with high area-efficiency and an order of 10^-6 for relative computational error.