RHCOS: An area-efficient reconfigurable high-precision solver for complex ordinary differential equations

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.