Diffsol is a library for solving ordinary differential equations (ODEs) or semi-explicit differential algebraic equations (DAEs) in Rust. You can use it out-of-the-box with vectors and matrices from the nalgebra or faer crates, or you can implement your own types by implementing the various vector and matrix traits in diffsol.

DiffSol implements the following solvers:

• A variable order Backwards Difference Formulae (BDF) solver, suitable for stiff problems and singular mass matrices.
• A Singly Diagonally Implicit Runge-Kutta (SDIRK or ESDIRK) solver, suitable for moderately stiff problems and singular mass matrices. You can use your own butcher tableau or use one of the provided (tr_bdf2 or esdirk34).
• A BDF solver that wraps the IDA solver solver from the Sundials library (requires the sundials feature). This is similar to the BDF solver above and is include for comparison purposes.

All solvers feature adaptive step-size control to given tolerances, dense output, event handling, stepping to specific times and forward sensitivity analysis. For comparison, the BDF solvers are similar to MATLAB's ode15s solver or the bdf solver in SciPy's solve_ivp function. The ESDIRK solver using the provided tr_bdf2 tableau is similar to MATLAB's ode23t solver.

Users can specify the equations to solve in the following ODE form:

where $M$ is a (possibly singular) mass matrix, $y$ is the state vector, $t$ is the time, $p$ is a vector of parameters, and $f$ is the right-hand side function. The mass matrix $M$ is optional (assumed to be the identity matrix if not provided).

See instructions on the crates.io page.

For more documentation and examples, see the API documentation.