Solving Differential Equations in<i>R</i>: Package<b>deSolve</b>

Soetaert, Karline; Petzoldt, Thomas; Setzer, R. Woodrow

doi:10.18637/jss.v033.i09

Cited by 1,128 publications

(574 citation statements)

References 18 publications

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“…Currently, most of the methods for stiff equations are wrapped methods (only the Rosenbrock with/without local extrapolation, and the order 1/2 BDF methods exist in native forms). While these methods, such as CVODE (provided by Sundials.jl 25 ) and radau (provided by ODEInterface.jl 26 ), are widely regarded standards for stiff ODEs, by not being native Julia functions these algorithms choices do not allow for the extra functionality such as arbitrary precision and arithmetic with physical units (these features require a pure-Julia implementation). Instead, since these are the standard algorithms wrapped in packages such as SciPy [15] and R's deSolve [26], the limitations of these wrapped solvers match the limitations of other common libraries.…”

Section: Limitations and Future Development Plansmentioning

confidence: 99%

DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia

Rackauckas

Nie

2017

JORS

1,096

877

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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.

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Section: Limitations and Future Development Plansmentioning

confidence: 99%

DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia

Rackauckas

Nie

2017

JORS

1,096

877

View full text Add to dashboard Cite

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“…Through the application of the R package ReacTran (Soetaert and Meysman, 2012), a sediment grid 10 m thick with 20 000 layers of identical thicknesses was generated. The finite difference approach transforms the partial differentials into ordinary differentials which are subsequently integrated by a stiff solver routine vode (Brown and Hindmarsh, 1989) within the R package DeSolve (Soetaert et al, 2010). Boundary conditions were chosen to reflect Permian oceanic conditions based on the current state of research (Sect.…”

Section: Numerical Solutions and Parametersmentioning

confidence: 99%

Latest Permian carbonate carbon isotope variability traces heterogeneous organic carbon accumulation and authigenic carbonate formation

et al. 2017

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Abstract. Bulk-carbonate carbon isotope ratios are a widely applied proxy for investigating the ancient biogeochemical carbon cycle. Temporal carbon isotope trends serve as a prime stratigraphic tool, with the inherent assumption that bulk micritic carbonate rock is a faithful geochemical recorder of the isotopic composition of seawater dissolved inorganic carbon. However, bulk-carbonate rock is also prone to incorporate diagenetic signals. The aim of the present study is to disentangle primary trends from diagenetic signals in carbon isotope records which traverse the Permian-Triassic boundary in the marine carbonate-bearing sequences of Iran and South China. By pooling newly produced and published carbon isotope data, we confirm that a global first-order trend towards depleted values exists. However, a large amount of scatter is superimposed on this geochemical record. In addition, we observe a temporal trend in the amplitude of this residual δ 13 C variability, which is reproducible for the two studied regions. We suggest that (sub-)sea-floor microbial communities and their control on calcite nucleation and ambient porewater dissolved inorganic carbon δ 13 C pose a viable mechanism to induce bulk-rock δ 13 C variability. Numerical model calculations highlight that early diagenetic carbonate rock stabilization and linked carbon isotope alteration can be controlled by organic matter supply and subsequent microbial remineralization. A major biotic decline among Late Permian bottom-dwelling organisms facilitated a spatial increase in heterogeneous organic carbon accumulation. Combined with low marine sulfate, this resulted in varying degrees of carbon isotope overprinting. A simulated time series suggests that a 50 % increase in the spatial scatter of organic carbon relative to the average, in addition to an imposed increase in the likelihood of sampling cements formed by microbial calcite nucleation to 1 out of 10 samples, is sufficient to induce the observed signal of carbon isotope variability. These findings put constraints on the application of Permian-Triassic carbon isotope chemostratigraphy based on whole-rock samples, which appears less refined than classical biozonation dating schemes. On the other hand, this signal of increased carbon isotope variability concurrent with the largest mass extinction of the Phanerozoic may proPublished by Copernicus Publications on behalf of the European Geosciences Union.

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“…We ran the model in r using ode for model integration and optim for parameter fitting (R Core Team, 2014;Soetaert et al, 2010).…”

Section: Model Calibrationmentioning

confidence: 99%

A Century of Legacy Phosphorus Dynamics in a Large Drainage Basin

McCrackin

Muller-Karulis

Gustafsson

et al. 2018

Global Biogeochemical Cycles

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There is growing evidence that the release of phosphorus (P) from "legacy" stores can frustrate efforts to reduce P loading to surface water from sources such as agriculture and human sewage. Less is known, however, about the magnitude and residence times of these legacy pools. Here we constructed a budget of net anthropogenic P inputs to the Baltic Sea drainage basin and developed a three-parameter, two-box model to describe the movement of anthropogenic P though temporary (mobile) and long-term (stable) storage pools. Phosphorus entered the sea as direct coastal effluent discharge and via rapid transport and slow, legacy pathways. The model reproduced past waterborne P loads and suggested an~30-year residence time in the mobile pool. Between 1900 and 2013, 17 and 27 Mt P has accumulated in the mobile and stable pools, respectively. Phosphorus inputs to the sea have halved since the 1980s due to improvements in coastal sewage treatment and reductions associated with the rapid transport pathway. After decades of accumulation, the system appears to have shifted to a depletion phase; absent further reductions in net anthropogenic P input, future waterborne loads could decrease. Presently, losses from the mobile pool contribute nearly half of P loads, suggesting that it will be difficult to achieve substantial near-term reductions. However, there is still potential to make progress toward eutrophication management goals by addressing rapid transport pathways, such as overland flow, as well as mobile stores, such as cropland with large soil-P reserves.Plain Language Summary All life depends on phosphorus (P), which is why it is an important crop fertilizer. Humans generally consume more P than needed and the excess ends up in sewage systems. Past management of P in fertilizer and human sewage has led to the accumulation of P in soils and sediments of lakes and streams. This accumulation is called "legacy" P because it can leak for decades to downstream lakes and coastal areas where it contributes to environmental problems. We developed a model to understand P dynamics for the entire drainage basin of the Baltic Sea since 1900. This model included a rapid transport pathway that represented sources such as runoff from cropland and a slow pathway that represented leakage from mobile legacy sources. The model suggests that loss from the mobile pool contributes about half of current waterborne inputs to the sea; as a result, it could be difficult to make substantial near-term reductions. However, there are opportunities to meet environmental goals by slowing the accumulation of P in the landscape and by implementing measures that address the rapid transport pathway, such runoff from cropland, and the mobile stores, such as cropland with large soil-P reserves.

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Solving Differential Equations inR: PackagedeSolve

Cited by 1,128 publications

References 18 publications

DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia

DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia

Latest Permian carbonate carbon isotope variability traces heterogeneous organic carbon accumulation and authigenic carbonate formation

A Century of Legacy Phosphorus Dynamics in a Large Drainage Basin

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