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 differentia...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Ubiquity Press
2017-05-01
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| Series: | Journal of Open Research Software |
| Subjects: | |
| Online Access: | http://openresearchsoftware.metajnl.com/articles/151 |
| _version_ | 1819230593710292992 |
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| author | Christopher Rackauckas Qing Nie |
| author_facet | Christopher Rackauckas Qing Nie |
| author_sort | Christopher Rackauckas |
| collection | DOAJ |
| description | 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. Funding statement: This work was partially supported by NIH grants P50GM76516 and R01GM107264 and NSF grants DMS1562176 and DMS1161621. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1321846, the National Academies of Science, Engineering, and Medicine via the Ford Foundation, and the National Institutes of Health Award T32 EB009418. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the NIH. |
| first_indexed | 2024-12-23T11:31:32Z |
| format | Article |
| id | doaj.art-2def322f009e4228822143064fda230b |
| institution | Directory Open Access Journal |
| issn | 2049-9647 |
| language | English |
| last_indexed | 2024-12-23T11:31:32Z |
| publishDate | 2017-05-01 |
| publisher | Ubiquity Press |
| record_format | Article |
| series | Journal of Open Research Software |
| spelling | doaj.art-2def322f009e4228822143064fda230b2022-12-21T17:48:48ZengUbiquity PressJournal of Open Research Software2049-96472017-05-015110.5334/jors.151122DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in JuliaChristopher Rackauckas0Qing Nie1Department of Mathematics, University of California-Irvine, Irvine, CA, 92697Department of Mathematics, University of California-Irvine, Irvine, CA, 92697DifferentialEquations.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. Funding statement: This work was partially supported by NIH grants P50GM76516 and R01GM107264 and NSF grants DMS1562176 and DMS1161621. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1321846, the National Academies of Science, Engineering, and Medicine via the Ford Foundation, and the National Institutes of Health Award T32 EB009418. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the NIH.http://openresearchsoftware.metajnl.com/articles/151Juliaordinary differential equationsstochastic differential equationspartial differential equationsmultiple dispatchmetaprogramminghigh-precisionmultithreading |
| spellingShingle | Christopher Rackauckas Qing Nie DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia Journal of Open Research Software Julia ordinary differential equations stochastic differential equations partial differential equations multiple dispatch metaprogramming high-precision multithreading |
| title | DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia |
| title_full | DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia |
| title_fullStr | DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia |
| title_full_unstemmed | DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia |
| title_short | DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia |
| title_sort | differentialequations jl a performant and feature rich ecosystem for solving differential equations in julia |
| topic | Julia ordinary differential equations stochastic differential equations partial differential equations multiple dispatch metaprogramming high-precision multithreading |
| url | http://openresearchsoftware.metajnl.com/articles/151 |
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