Parallel Solution Method for Hamiltonian Equations Based on FPGA and Matlab Programming Verification

Differential equations play an important role in the fields of artificial intelligence, image processing, and aerospace, and the solution of differential equations is the mathematical basis for research in each field. Traditional numerical methods can approximate the solution of complex differential equations, but there is a problem of accuracy loss in solving systems that do not have asymptotic stability. As a numerical algorithm that preserves the structural properties of Sin, the Sin algorithm has shown advantages in tracking Hamiltonian systems over long periods. However, few studies on the acceleration of the Sim algorithm for Hamiltonian systems do not possess asymptotic stability. To this end, an improved refined Sim algorithm is proposed in this paper and its effectiveness is verified by MATLAB. In addition, an improved fine Sim algorithm IP based on FPGA devices is constructed and its accuracy and parallel acceleration are verified on a hardware platform. This study provides ideas for the research of accelerated computation of the Xin algorithm for Hamiltonian systems without asymptotic stability, which is important for improving the efficiency of numerical solutions.