In this paper, the performance characteristics of different solution techniques and program packages to solve a large number of independent ordinary differential equation systems is examined. The employed hardware are an Intel Core i7-4820K CPU with 30.4 GFLOPS peak double-precision performance per cores and an Nvidia GeForce Titan Black GPU that has a total of 1707 GFLOPS peak double-precision performance. The tested systems (Lorenz equation, Keller--Miksis equation and a pressure relief valve model) are non-stiff and have low dimension. Thus, the performance of the codes are not limited by memory bandwidth, and Runge--Kutta type solvers are efficient and suitable choices. The tested program packages are MPGOS written in C++ and specialised only for GPUs; ODEINT implemented in C++, which supports execution on both CPUs and GPUs; finally, DifferentialEquations.jl written in Julia that also supports execution on both CPUs and GPUs. Using GPUs, the program package MPGOS is superior. For CPU computations, the ODEINT program package has the best performance.

中文翻译：

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在 GPU 和 CPU 上求解大量非刚性、低维常微分方程组：MPGOS、ODEINT 和 DifferentialEquations.jl 的性能比较

在本文中，研究了求解大量独立常微分方程组的不同求解技术和程序包的性能特征。所采用的硬件是英特尔酷睿 i7-4820K CPU，每个内核具有 30.4 GFLOPS 峰值双精度性能，以及具有总计 1707 GFLOPS 峰值双精度性能的 Nvidia GeForce Titan Black GPU。被测试的系统（洛伦兹方程、Keller--Miksis 方程和减压阀模型）是非刚性的并且具有低尺寸。因此，代码的性能不受内存带宽的限制，Runge--Kutta 型求解器是高效且合适的选择。测试的程序包是用C++编写的MPGOS，专门用于GPU；ODEINT 用 C++ 实现，支持在 CPU 和 GPU 上执行；最后，用 Julia 编写的 DifferentialEquations.jl 也支持在 CPU 和 GPU 上执行。使用GPU，程序包MPGOS 更胜一筹。对于 CPU 计算，ODEINT 程序包具有最佳性能。