differential-equations

• Ordinary Differential Equations (ODEs) - Fixed-step and adaptive solvers with comprehensive features including event detection, dense output, and customizable and common recipes for solution output.

  • Initial Value Problems - Solve problems with known initial conditions
  • Boundary Value Problems - Solve endpoint-constrained ODE problems with BVP::ode and the same final-trajectory output controls used by IVPs

• Differential Algebraic Equations (DAEs) - Implicit differential algebraic equations in the form $M f \prime = f(t,y)$ where $M$ can be singular

  • Index-1,2,3 DAEs - Index-1 implicitly supported, higher index equations require declaration in solver.

• Delay Differential Equations (DDEs) - Adaptations of ODE solvers to handle delay differential equations by tracking history for interpolation.

  • Fixed-Delay Problems - Solve problems with fixed delays
  • Variable-Delay Problems - Solve problems with state driven delays

• Stochastic Differential Equations (SDEs) - Fixed step explicit Runge-Kutta methods for stochastic differential equations.

  • Customizable Noise - User implements noise in SDE implementation

• Partial Differential Equations (PDEs) - Spatial discretization backends for time-dependent PDEs.

  • Method of Lines - Discretize general conservative PDEs on structured grids with finite difference or finite volume schemes, then reuse existing ODE IVP solvers.
  • Finite Volume - Conservation-law backend with MUSCL reconstruction, limiters, and numerical fluxes.
  • Yee Grid - Specialized staggered FDTD grid for Maxwell's equations.

Feature Flags

• nalgebra: Enables nalgebra matrix and vector states, including fixed-size and dynamic matrices.
• num-complex: Enables complex number states.
• ndarray: Enables ndarray array states.
• faer: Enables faer matrix states.
• polars: Enables converting solutions to Polars data frames.
• serde: Enables solution serialization and deserialization.

The polars feature requires Rust 1.95 or newer.

Contributing

This library is looking for contributions to bring the future of scientific computing to Rust!

Please see CONTRIBUTING.md for more information on how to contribute to this project.

Custom states derived with #[derive(State)] can contain Vec<T> fields. Their lengths are determined at runtime, and zeros_like() preserves those lengths. See dynamic state fields.