Common Solver Options (Solve Keyword Arguments)

:auto vs :nonstiff vs :stiff - Denotes the equation as nonstiff/stiff. :auto allow the default handling algorithm to choose stiffness detection algorithms. The default handling defaults to using :auto.

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

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

:additive - Denotes that the underlying SDE has additive noise.

:stratonovich - Denotes that the solution should adhere to the Stratonovich interpretation.

dense: Denotes whether to save the extra pieces required for dense (continuous) output. Default is save_everystep && isempty(saveat) for algorithms which have the ability to produce dense output, i.e. by default it’s true unless the user has turned off saving on steps or has chosen a saveat value. If dense=false, the solution still acts like a function, and sol(t) is a linear interpolation between the saved time points.

saveat: Denotes specific 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 available to the solver. If only saveat is given, then the arguments save_everystep and dense are false by default. If saveat is given a number, then it will automatically expand to tspan[1]:saveat:tspan[2]. For methods where interpolation is not possible, saveat may be equivalent to tstops. The default value is [].

save_idxs: Denotes the indices for the components of the equation to save. Defaults to saving all indices. For example, if you are solving a 3-dimensional ODE, and given save_idxs = [1, 3], only the first and third components of the solution will be outputted. Notice that of course in this case the outputted solution will be two-dimensional.

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 [].

save_everystep: Saves the result at every step. Default is true if isempty(saveat).

save_on: Denotes whether intermediate solutions are saved. This overrides the settings of dense, saveat and save_everystep and is used by some applications to manually turn off saving temporarily. Everyday use of the solvers should leave this unchanged. Defaults to true.

save_start: Denotes whether the initial condition should be included in the solution type as the first timepoint. Defaults to true.

save_end: Denotes whether the final timepoint is forced to be saved, regardless of the other saving settings. Defaults to true.

initialize_save: Denotes whether to save after the callback initialization phase (when u_modified=true). Defaults to true.

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

abstol: Absolute tolerance in adaptive timestepping. This is the tolerance on local error estimates, not necessarily the global error (though these quantities are related). Defaults to 1e-6 on deterministic equations (ODEs/DDEs/DAEs) and 1e-2 on stochastic equations (SDEs/RODEs).

reltol: Relative tolerance in adaptive timestepping. This is the tolerance on local error estimates, not necessarily the global error (though these quantities are related). Defaults to 1e-3 on deterministic equations (ODEs/DDEs/DAEs) and 1e-2 on stochastic equations (SDEs/RODEs).

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

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

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

force_dtmin: Declares whether to continue, forcing the minimum dt usage. Default is false, which has the solver throw a warning and exit early when encountering the minimum dt. Setting this true allows the solver to continue, never letting dt go below dtmin (and ignoring error tolerances in those cases). Note that true is not compatible with most interop packages.

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.

internalnorm: The norm function internalnorm(u,t) which error estimates are calculated. Required are two dispatches: one dispatch for the state variable and the other on the elements of the state variable (scalar norm). Defaults are package-dependent.

controller: Possible examples are IController, PIController, PIDController, PredictiveController. Default is algorithm-dependent.

gamma: The risk-factor γ in the q equation for adaptive timestepping of the controllers using it. Default is algorithm-dependent.

beta1: The Lund stabilization α parameter. Default is algorithm-dependent.

beta2: The Lund stabilization β parameter. Default is algorithm-dependent.

qmax: Defines the maximum value possible for the adaptive q. Default is algorithm-dependent.

qmin: Defines the minimum value possible for the adaptive q. Default is algorithm-dependent.

qsteady_min: Defines the minimum for the range around 1 where the timestep is held constant. Default is algorithm-dependent.

qsteady_max: Defines the maximum for the range around 1 where the timestep is held constant. Default is algorithm-dependent.

qoldinit: The initial qold in stabilization stepping. Default is algorithm-dependent.

failfactor: The amount to decrease the timestep by if the Newton iterations of an implicit method fail. Default is 2.

calck: Turns on and off the internal ability for intermediate interpolations (also known as intermediate density). Not the same as dense, which is post-solution interpolation. 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 nowhere else. Note that this is only required if the algorithm doesn’t have a free or lazy interpolation (DP8()). If calck = false, saveat cannot be used. The rare keyword calck can be useful in event handling.

alias_u0: allows the solver to alias the initial condition array that is contained in the problem struct. Defaults to false.

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(u,p,t) where, when it returns true, it will reject the timestep. Disabled by default.

unstable_check: Specifies a function unstable_check(dt,u,p,t) where, when it returns true, it will cause the solver to exit and throw a warning. Defaults to any(isnan,u), i.e. checking if any value is a NaN.

verbose: Toggles whether warnings are thrown when the solver exits early. Defaults to true.

merge_callbacks: Toggles whether to merge prob.callback with the solve keyword argument callback. Defaults to true.

wrap: Toggles whether to wrap the solution if prob.problem_type has a preferred alternate wrapper type for the solution. Useful when speed, but not shape of solution is important. Defaults to Val(true). Val(false) will cancel wrapping the solution.

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.

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.