Displaying 1 to 20 from 21 results

DifferentialEquations.jl - Julia suite for high-performance solvers of differential equations

  •    Julia

The well-optimized DifferentialEquations solvers benchmark as the some of the fastest implementations, using classic algorithms and ones from recent research which routinely outperform the "standard" C/Fortran methods, and include algorithms optimized for high-precision and HPC applications. At the same time, it wraps the classic C/Fortran methods, making it easy to switch over to them whenever necessary. It integrates with the Julia package sphere, for example using Juno's progress meter, automatic plotting, built-in interpolations, and wraps other differential equation solvers so that many different methods for solving the equations can be accessed by simply switching a keyword argument. It utilizes Julia's generality to be able to solve problems specified with arbitrary number types (types with units like Unitful, and arbitrary precision numbers like BigFloats and ArbFloats), arbitrary sized arrays (ODEs on matrices), and more. This gives a powerful mixture of speed and productivity features to help you solve and analyze your differential equations faster. For information on using the package, see the stable documentation. Use the latest documentation for the version of the documentation which contains the un-released features.




brian2 - Brian is a free, open source simulator for spiking neural networks.

  •    Python

Brian is a free, open source simulator for spiking neural networks. It is written in the Python programming language and is available on almost all platforms. We believe that a simulator should not only save the time of processors, but also the time of scientists. Brian is therefore designed to be easy to learn and use, highly flexible and easily extensible. Brian2 is released under the terms of the CeCILL 2.1 license.

ode-rk4 - Integrate a system of ODEs using the Fourth Order Runge-Kutta (RK-4) method

  •    Javascript

For a similar adaptive method using the fifth order Cash-Karp Runge-Kutta method with fourth order embedded error estimator, see ode45-cash-karp.Returns: Initialized integrator object.

ode45-cash-karp - Integrate a system of Ordinary Differential Equations using the Fifth Order Adaptive Cash-Karp method

  •    Javascript

where is a vector of length . Given time step , the Cash-Karp method uses a fifth order Runge-Kutta scheme with a fourth order embedded estimator in order to control the error. In other words, the same intermediate values used in calculating the fifth order update can be used to calculate a fourth order estimate. The difference yields an error estimate, and the error estimate controls the timestep .Initialized integrator object.


DASKR.jl - Interface to DASKR, a differential algebraic system solver

  •    Fortran

A solver for differential algebraic equations (DAE). This wraps the original DASKR FORTRAN solver. DASKR is a derivative of the DASSL solver with root finding. An interface to the JuliaDiffEq common interface is also provided.

DiffEqCallbacks.jl - A library of useful callbacks for DiffEq solvers

  •    Julia

This is a library of callbacks for extending the solvers of DifferentialEquations.jl. For more information on using callbacks, see the manual page.

DiffEqJump

  •    Julia

DiffEqJump.jl is a component package in the DifferentialEquations ecosystem. It holds the utilities for building jump equations, like Gillespie SSA and jump diffusions. Users interested in using this functionality should check out DifferentialEquations.jl.

diffeqr - Solving differential equations in R using DifferentialEquations.jl

  •    R

diffeqr is a package for solving differential equations in R. It utilizes DifferentialEquations.jl for its core routines to give high performance solving of ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), and differential-algebraic equations (DAEs) directly in R. If you have any questions, or just want to chat about solvers/using the package, please feel free to chat in the Gitter channel. For bug reports, feature requests, etc., please submit an issue.

ParameterizedFunctions.jl - Functions with parameters for differential equations

  •    Julia

ParameterizedFunctions.jl is a component of the JuliaDiffEq ecosystem which allows for parameters to be explicitly present within functions. The interface which ParameterizedFunctions describes allows for functionality which requires parameters, such as parameter sensitivity analysis and parameter estimation, to be added to the differential equation solvers of DifferentialEquations.jl. While the interface itself is of importance to ecosystem developers, ParameterizedFunctions.jl provides user-facing macros which make a ParameterizedFunction easy to define, and automatically include optimizations like explicit Jacobian functions and explicit inverse Jacobian functions for the differential equation solvers to take advantage of. The result is an easy to use API which allows for more functionality and more performance optimizations than could traditionally be offered. ParameterizedFunction is a type which can be used in various JuliaDiffEq solvers where the parameters must be accessible by the solver function. These use call overloading generate a type which acts like a function f(t,u,du) but has access to many more features. For example, a ParameterizedFunction can contain a function for the Jacobian or Inverse Jacobian. If such functions exist, the solvers can use them to increase the speed of computations. If they don't exist, the solvers will ignore them. Since ParameterizedFunction is a subtype of Function, these can be used anywhere that a function can be used, just with the extra functionality ignored.

double_pendulum - Animations of random double pendulums

  •    Python

The code behind @pendulum_bot Twitter bot which posts animations of a double pendulum released from a random position to swing for 30 seconds. The animation is saved as .mp4 video in animations subdirectory.

ODEInterfaceDiffEq.jl - Adds the common API onto ODEInterface

  •    Julia

This package contains bindings for ODEInterface.jl to allow it to be used with the JuliaDiffEq common interface. For more information on using the solvers from this package, see the DifferentialEquations.jl documentation. The options available in solve are documented at the common solver options page. The available methods are documented at the ODE solvers page.

godesim - ODE system solver made simple. For IVPs (initial value problems).

  •    Go

Wrangle non-linear differential equations while writing maintainable, simple code. ODE solvers seem to fill the niche of simple system solvers in your numerical packages such as scipy's odeint/solve_ivp.

FasterNeuralDiffEq - Code for "'Hey, that's not an ODE:' Faster ODE Adjoints via Seminorms" (ICML 2021)

  •    Python

Backpropagation through a Neural ODE/CDE can be performed via the "adjoint method", which involves solving another differential equation backwards in time. However it turns out that default numerical solvers are unnecessarily stringent when solving the adjoint equation, and take too many steps, that are too small. That's it.






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