DifferentialEquations.jl

DifferentialEquations.jl - A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia. DifferentialEquations.jl is a package for solving differential equations in Julia. It covers discrete equations (function maps, discrete stochastic (Gillespie/Markov) simulations), ordinary differential equations, stochastic differential equations, algebraic differential equations, delay differential equations, hybrid differential equations, jump diffusions, and (stochastic) partial differential equations. Through extensive use of multiple dispatch, metaprogramming, plot recipes, foreign function interfaces (FFI), and call-overloading, DifferentialEquations.jl offers a unified user interface to solve and analyze various forms of differential equations while not sacrificing features or performance. Many modern features are integrated into the solvers, such as allowing arbitrary user-defined number systems for high-precision and arithmetic with physical units, built-in multithreading and parallelism, and symbolic calculation of Jacobians. Integrated into the package is an algorithm testing and benchmarking suite to both ensure accuracy and serve as an easy way for researchers to develop and distribute their own methods. Together, these features build a highly extendable suite which is feature-rich and highly performant.


References in zbMATH (referenced in 58 articles )

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  1. Antoñana, Mikel; Chartier, Philippe; Murua, Ander: Majorant series for the (N)-body problem (2022)
  2. Bitsouni, Vasiliki; Tsilidis, Vasilis: Mathematical modeling of tumor-immune system interactions: the effect of rituximab on breast cancer immune response (2022)
  3. Chan, Jesse; Taylor, Christina G.: Efficient computation of Jacobian matrices for entropy stable summation-by-parts schemes (2022)
  4. James Gardner, Oscar A. Douglas-Gallardo, Wojciech G. Stark, Julia Westermayr, Svenja M. Janke, Scott Habershon, Reinhard J. Maurer: NQCDynamics.jl: A Julia Package for Nonadiabatic Quantum Classical Molecular Dynamics in the Condensed Phase (2022) arXiv
  5. Taylor McDonnell; Andrew Ning: GXBeam: A Pure Julia Implementation of Geometrically Exact Beam Theory (2022) not zbMATH
  6. Ylinen, Lauri; von Lerber, Tuomo; Küppers, Franko; Lassas, Matti: Analysis of a dynamical system modeling lasers and applications for optical neural networks (2022)
  7. Zhang, Hong; Constantinescu, Emil M.; Smith, Barry F.: \textttPETScTSAdjoint: a discrete adjoint ODE solver for first-order and second-order sensitivity analysis (2022)
  8. Alvestad, Daniel; Larsen, Rasmus; Rothkopf, Alexander: Stable solvers for real-time complex Langevin (2021)
  9. Augustinas Sukys, Ramon Grima: MomentClosure.jl: automated moment closure approximations in Julia (2021) arXiv
  10. Browning, Alexander P.; Maclaren, Oliver J.; Buenzli, Pascal R.; Lanaro, Matthew; Allenby, Mark C.; Woodruff, Maria A.; Simpson, Matthew J.: Model-based data analysis of tissue growth in thin 3D printed scaffolds (2021)
  11. Cancès, Eric; Fermanian Kammerer, Clotilde; Levitt, Antoine; Siraj-Dine, Sami: Coherent electronic transport in periodic crystals (2021)
  12. David Plankensteiner, Christoph Hotter, Helmut Ritsch: QuantumCumulants.jl: A Julia framework for generalized mean-field equations in open quantum systems (2021) arXiv
  13. Han Veiga, Maria; Öffner, Philipp; Torlo, Davide: DeC and ADER: similarities, differences and a unified framework (2021)
  14. Hegedűs, Ferenc: Program package MPGOS: challenges and solutions during the integration of a large number of independent ODE systems using GPUs (2021)
  15. Hendrik Ranocha: SummationByPartsOperators.jl: A Julia library of provably stable discretization techniques with mimetic properties (2021) not zbMATH
  16. Korolev, Ivan: Identification and estimation of the SEIRD epidemic model for COVID-19 (2021)
  17. Kulyabov, D. S.; Korol’kova, A. V.: Computer algebra in Julia (2021)
  18. Lindner, Michael; Lincoln, Lucas; Drauschke, Fenja; Koulen, Julia M.; Würfel, Hans; Plietzsch, Anton; Hellmann, Frank: NetworkDynamics.jl -- composing and simulating complex networks in Julia (2021)
  19. López, Oscar; Oleaga, Gerardo; Sánchez, Alejandra: Markov-modulated jump-diffusion models for the short rate: pricing of zero coupon bonds and convexity adjustment (2021)
  20. Michael Schlottke-Lakemper; Gregor Gassner; Hendrik Ranocha; Andrew Winters; et al.: Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing (2021) arXiv

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