Common Solver Options

The DifferentialEquations.jl universe has a large set of common arguments available for the solve function. These arguments apply to solve on any problem type and are only limited by limitations of the specific implementations.

Many of the defaults depend on the algorithm or the package the algorithm derives from. Not all of the interface is provided by every algorithm. For more detailed information on the defaults and the available options for specific algorithms / packages, see the manual pages for the solvers of specific problems.

Default Algorithm Hinting

To help choose the default algorithm, the keyword argument alg_hints is provided. alg_hints is a Vector{Symbol} which describe the problem at a high level to the solver. The options are:

• :nonstiff - Denotes the equation as nonstiff.

• :stiff - Denotes the equation as stiff.

Currently unused options include:

• :interpolant - Denotes that a high-precision interpolation is important.

• :memorybound - Denotes that the solver will be memory bound.

This functionality is derived via the benchmarks in DiffEqBenchmarks.jl and is under active development.

Output Control

These arguments control the output behavior of the solvers. It defaults to maximum output to give the best interactive user experience, but can be reduced all the way to only saving the solution at the final timepoint. All of these options can be mixed and matched. For example, the combination:

saveat=[0:1/4:1],save_timeseries=false,dense=false

will only save the solution at the timepoints 0:1/4:1 and no other locations. For more examples for controlling the output behavior, see the Output Specification manual page.

• dense: Denotes whether to save the extra pieces for dense (continuous) output. Default is true for algorithms which have the ability to produce dense output.

• saveat: Denotes extra times to save the solution at during the solving phase. The solver will save at each of the timepoints in this array in the most efficient manner. Note that this can be used even if dense=false. For methods where interpolation is not possible, this may be equivalent to tstops. Default is [].

• tstops: Denotes extra times that the timestepping algorithm must step to. This should be used to help the solver deal with discontinuities and singularities, since stepping exactly at the time of the discontinuity will improve accuracy. If a method cannot change timesteps (fixed timestep multistep methods), then tstops will use an interpolation, matching the behavior of saveat. If a method cannot change timesteps and also cannot interpolate, then tstops must be a multiple of dt or else an error will be thrown. Default is [].

• d_discontinuities: Denotes locations of discontinuities in low order derivatives. This will force FSAL algorithms which assume derivative continuity to re-evaluate the derivatives at the point of discontinuity. The default is [].

• calck: Turns on and off the internal ability for intermediate interpolations. This defaults to dense || !isempty(saveat) || "no custom callback is given". This can be used to turn off interpolations (to save memory) if one isn't using interpolations when a custom callback is used. Another case where this may be used is to turn on interpolations for usage in the integrator interface even when interpolations are used no where else. Note that this is only required if the algorithm doesn't have a free or lazy interpolation (DP8()).

• save_timeseries: Saves the result at every timeseries_steps iteration. Default is true.

• timeseries_steps: Denotes how many steps between saving a value for the timeseries. Defaults to 1.

Stepsize Control

These arguments control the timestepping routines.

• adaptive: Turns on adaptive timestepping for appropriate methods. Default is true.

• abstol: Absolute tolerance in adaptive timestepping. Defaults to 1e-3.

• reltol: Relative tolerance in adaptive timestepping. Defaults to 1e-6.

• dt: Sets the initial stepsize. This is also the stepsize for fixed timestep methods. Defaults to an automatic choice.

• internalnorm: The norm function internalnorm(u) which error estimates are calculated. Defaults are package-dependent.

• gamma: The risk-factor γ in the q equation for adaptive timestepping. Default is algorithm dependent.

• dtmax: Maximum dt for adaptive timestepping. Defaults are package-dependent.

• dtmin: Minimum dt for adaptive timestepping. Defaults are package-dependent.

• beta1: The Lund stabilization α parameter. Defaults are algorithm-dependent.

• beta2: The Lund stabilization β parameter. Defaults are algorithm-dependent.

• qmax: Defines the maximum value possible for the adaptive q. Defaults are algorithm-dependent.

• qmin: Defines the maximum value possible for the adaptive q. Defaults are algorithm-dependent.

• qoldinit: The initial qold in stabilization stepping. Defaults are algorithm-dependent.

Fixed Stepsize Usage

Note that if a method does not have adaptivity, the following rules apply:

• If dt is set, then the algorithm will step with size dt each iteration.

• If tstops and dt are both set, then the algorithm will step with either a size dt, or use a smaller step to hit the tstops point.

• If tstops is set without dt, then the algorithm will step directly to each value in tstops

• If neither dt nor tstops are set, the solver will throw an error.

Miscellaneous

• maxiters: Maximum number of iterations before stopping. Defaults to 1e5.

• callback: Specifies a callback. Defaults to a callback function which performs the saving routine. For more information, see the Event Handling and Callback Functions manual page.

• isoutofdomain: Specifies a function isoutofdomain(t,u) where, when it returns false, it will reject the timestep. Defaults to always false.

Progress Monitoring

These arguments control the usage of the progressbar in the Juno IDE.

• progress: Turns on/off the Juno progressbar. Default is false.

• progress_steps: Numbers of steps between updates of the progress bar. Default is 1000.

• progress_name: Controls the name of the progressbar. Default is the name of the problem type.

• progress_message: Controls the message with the progressbar. Defaults to showing dt, t, the maximum of u.

User Data

• userdata: This is a user-chosen type which will show up in the integrator type, allowing the user to have a cache for callbacks, event handling, and other various activities.

Error Calculations

If you are using the test problems (ex: ODETestProblem), then the following options control the errors which are calculated:

• timeseries_errors: Turns on and off the calculation of errors at the steps which were taken, such as the l2 error. Default is true.

• dense_errors: Turns on and off the calculation of errors at the steps which require dense output and calculate the error at 100 evenly-spaced points throughout tspan. An example is the L2 error. Default is false.