OrdinaryDiffEqTsit5

The Tsitouras 5/4 method is the recommended default solver for most non-stiff differential equation problems. This method provides an excellent balance of efficiency, reliability, and accuracy.

Key Properties

Tsit5 offers:

• Fifth-order accuracy with embedded fourth-order error estimation
• Excellent efficiency at default tolerances (1e-6 to 1e-3)
• FSAL (First Same As Last) property for computational efficiency
• High-quality interpolation for dense output
• Robust performance across a wide range of problem types
• Optimized coefficients for minimal error in practical applications

When to Use Tsit5

Tsit5 is recommended for:

• Most non-stiff problems as the first choice solver
• Default and higher tolerances (1e-3 to 1e-6)
• General-purpose integration when problem characteristics are unknown
• Educational and research applications as a reliable baseline
• Real-time applications requiring predictable performance
• Problems where simplicity and reliability are preferred over maximum efficiency

Solver Selection Guide

Primary recommendation

• Tsit5: Use as the default choice for non-stiff problems at standard tolerances

Automatic switching

• AutoTsit5: Automatically switches to a stiff solver when stiffness is detected, making it robust for problems of unknown character

When to Consider Alternatives

Consider other solvers when:

• Higher accuracy needed: Use Verner methods (Vern6, Vern7, Vern8, Vern9) for tolerances below 1e-6
• Higher tolerances: Use BS3 or OwrenZen3 for tolerances above 1e-3
• Robust error control needed: Use BS5 when Tsit5 struggles with error estimation
• Equation is stiff: Use implicit methods (SDIRK, BDF) or semi-implicit methods (Rosenbrock) for stiff problems
• Special properties required: Use specialized methods (SSP, symplectic, etc.) for specific problem types

Installation

To be able to access the solvers in OrdinaryDiffEqTsit5, you must first install them use the Julia package manager:

using Pkg
Pkg.add("OrdinaryDiffEqTsit5")

This will only install the solvers listed at the bottom of this page. If you want to explore other solvers for your problem, you will need to install some of the other libraries listed in the navigation bar on the left.

Example usage

using OrdinaryDiffEqTsit5

function lorenz!(du, u, p, t)
    du[1] = 10.0 * (u[2] - u[1])
    du[2] = u[1] * (28.0 - u[3]) - u[2]
    du[3] = u[1] * u[2] - (8 / 3) * u[3]
end
u0 = [1.0; 0.0; 0.0]
tspan = (0.0, 100.0)
prob = ODEProblem(lorenz!, u0, tspan)
sol = solve(prob, Tsit5())

Full list of solvers

Tsit5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
        thread = OrdinaryDiffEq.False())

AutoTsit5(stiff_alg; kwargs...)