From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 51594 invoked by alias); 22 Oct 2017 10:30:57 -0000 Mailing-List: contact gsl-discuss-help@sourceware.org; run by ezmlm Precedence: bulk List-Id: List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sourceware.org Received: (qmail 51579 invoked by uid 89); 22 Oct 2017 10:30:56 -0000 Authentication-Results: sourceware.org; auth=none X-Virus-Found: No X-Spam-SWARE-Status: No, score=0.9 required=5.0 tests=BAYES_50,RCVD_IN_DNSWL_LOW,SPF_NEUTRAL autolearn=ham version=3.3.2 spammy=H*F:D*fi, christopher, tolerance, ODE X-HELO: gw02.mail.saunalahti.fi Received: from gw02.mail.saunalahti.fi (HELO gw02.mail.saunalahti.fi) (195.197.172.116) by sourceware.org (qpsmtpd/0.93/v0.84-503-g423c35a) with ESMTP; Sun, 22 Oct 2017 10:30:54 +0000 Received: from [192.168.0.110] (a91-152-223-20.elisa-laajakaista.fi [91.152.223.20]) by gw02.mail.saunalahti.fi (Postfix) with ESMTP id F3E784009F; Sun, 22 Oct 2017 13:30:49 +0300 (EEST) From: Tuomo Keskitalo Subject: GSL ODE-solvers' status To: GSL Discuss Mailing List Message-ID: Date: Sun, 22 Oct 2017 10:30:00 -0000 User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101 Thunderbird/52.4.0 MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 7bit X-SW-Source: 2017-q4/txt/msg00000.txt.bz2 Dear all, Patrick found this recent blog post by Christopher Rackauckas, who is the developer of DifferentialEquations.jl, which contains a wide selection of ODE-solvers for Julia: http://www.stochasticlifestyle.com/comparison-differential-equation-solver-suites-matlab-r-julia-python-c-fortran/ Christopher also has given an informative talk at the Julia Developers conference: https://www.juliabloggers.com/video-introduction-to-differentialequations-jl/ I'm happy to see that there has been at least some progress on ODE solving methods! Unfortunately, I am no longer really up-to-date with this field. If someone has the opportunity to work on GSL ODE-solvers, I try to point towards potential places of improvement. The methods suggested by Cristoph in his presentation are: On explicit side: - Bogacki-Shampine 3/2 method - Tsitouras 5/4 Runge-Kutta method - Verner 7/6 Runge-Kutta method On implicit side: - Rosenbrock 2/3 method - Radau IIA Runge-Kutta variable order method - CVODE_BDF. GSL's msbdf is based on this method. More information on these are surely available in DifferentialEquations.jl source codes. Also, for time stepping, there appears to be some PI-controller based method for adjusting step size, which is very interesting. Finally, Cristoph does not talk in favor of extrapolation methods, but I have previously wondered how much better bsimp would fare, if the internal iteration would be modified so that it continues only up to user given tolerances, instead of near machine precision. It would be interesting to see if these (old and) new methods would yield significant improvements compared to those existing now in ode-initval2, or would improvements remain marginal? As for GSL ode-initval2 framework: Room for improvement exists in better co-operation of GSL stepper and control routines. For multistep methods, it is not good that method order is adjusted internally by stepper and step size is adjusted independently by control routines. Final tip for all ODE-solver users: Benchmark different steppers for your problem. Depending on the problem and your tolerance requirements, you may get significant improvements just by changing the stepper. BR, Tuomo -- Tuomo.Keskitalo@iki.fi http://iki.fi/tuomo.keskitalo