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In this paper, the performance characteristics of different solutiontechniques and program packages to solve a large number of independent ordinarydifferential equation systems is examined. The employed hardware are an IntelCore i7-4820K CPU with 30.4 GFLOPS peak double-precision performance per coresand an Nvidia GeForce Titan Black GPU that has a total of 1707 GFLOPS peakdouble-precision performance. The tested systems (Lorenz equation,Keller--Miksis equation and a pressure relief valve model) are non-stiff andhave low dimension. Thus, the performance of the codes are not limited bymemory bandwidth, and Runge--Kutta type solvers are efficient and suitablechoices. The tested program packages are MPGOS written in C++ and specialisedonly for GPUs; ODEINT implemented in C++, which supports execution on both CPUsand GPUs; finally, DifferentialEquations.jl written in Julia that also supportsexecution on both CPUs and GPUs. Using GPUs, the program package MPGOS issuperior. For CPU computations, the ODEINT program package has the bestperformance.

Solving large number of non-stiff, low-dimensional ordinary differential  equation systems on GPUs and CPUs: performance comparisons of MPGOS, ODEINT  and DifferentialEquations.jl