A Simple Numerical Solution Framework for Ordinary Differential Equations Based on Reduced MIPS Instructions

Abstract

Recently, numerical solutions for Ordinary Differential Equations (ODEs) based on fourth-order Runge-Kutta method and fast Euler method are becoming more popular, however, necessary large memory and great volume of floating-point operations bring a high burden to traditional CPU. To attack this, a simple ODE numerical solution framework supporting both Euler method and fourth-order Runge-Kutta method is proposed. The framework includes three-level work: (1) in the algorithm level, the calculation principles and characteristics of Euler method and fourth-order Runge-Kutta method are analyzed; (2) in the hardware level, floating-point calculation units meeting IEEE 754 standard based on the reduced MIPS instruction set are worked out; (3) in the software level, a Linux server based on PYNQ device is built, so users can call the system through python programming. The calculation accuracy of the proposed framework is comparable to that of software calculation, and the framework has a maximum acceleration effect of 38 times compared to the pure PS ARM CPU.