Features.

Numra covers the equation classes that scientific computing depends on, with a unified API surface. Each feature here links to its full chapter in the book.

Equation classes.

• ODE — explicit (Tsit5, DoPri5, Verner 6/7/8), implicit (Radau5, ESDIRK 32/43/54), multistep (BDF), automatic stiffness selection.
• SDE — Euler-Maruyama, Milstein, stochastic Runge-Kutta; weak and strong convergence orders documented per method.
• DDE — delay differential equations with continuous extensions for past-state interpolation.
• FDE — fractional differential equations with memory-efficient Caputo-derivative methods.
• IDE — integro-differential equations.
• PDE — method-of-lines and finite-difference stencils for parabolic and hyperbolic problems.
• SPDE — stochastic partial differential equations.

Cross-cutting capabilities.

• Dense output and event detection across all explicit ODE solvers.
• Adaptive integration with proportional-integral step control.
• Linear algebra (faer-backed), nonlinear solvers, automatic differentiation.
• Quadrature, interpolation, FFT, statistics, signal processing, curve fitting.
• Optimization and optimal control.
• Generic over scalar (f32 and f64); numra-core is no_std-compatible.

What Numra does not do.

Numra is intentionally a numerical-methods library, not a symbolic-math system or a general PDE framework. Symbolic manipulation, mesh generation, and finite-element assembly live elsewhere; Numra integrates with them through plain Rust interfaces.

The full solver inventory is documented in the solver reference chapter of the book, with literature citations for each method.