Acceleration of the Precise Integration Method for Initial Value Problems Based on ACAP

This paper investigates the numerical implementation of solving initial value problems (IVPs) using the Precise Integration Method (PIM). For the solution of IVPs, PIM employs a recursive calculation based on matrix exponentiation, effectively avoiding the error accumulation often encountered in conventional numerical methods. The study focuses on the implementation of this method on a CPU, as well as its hardware-accelerated implementation on an Adaptive Compute Acceleration Platform (ACAP). By leveraging the powerful parallel processing capabilities of ACAP programmable logic (PL) and AI engines (AIE), the efficiency of complex numerical computations is significantly improved. Compared to traditional CPU platforms, ACAP demonstrates superior performance in large-scale computational tasks.