Scientific Computing in Rust

Features

• Initial value problem solving
• Root finding algorithms
• Polynomials
• Polynomial Interpolation
• Scientific Constants
• Special functions/polynomials
• Numeric quadrature
• Numeric differentiation

Explanations of the features can be found here.

Initial Value Problems

There are two adaptive Runge-Kutta methods, two Adams predictor-correctors, and two adaptive Backwards Differentiation Formulas implemented. The interface to all of the solvers is the same. As an example, this code solves y' = y using the Runge-Kutta-Fehlberg method.

```rust use bacon_sci::ivp::{RK45, RungeKuttaSolver}; use nalgebra::SVector;

fn deriv(t: f64, y: &[f64], _params: &mut ()) -> Result, String> { Ok(SVector::::fromcolumn_slice(y)) }

fn solve() -> Result<(), String> { let solver = RK45::new() .withdtmin(0.01)? .withdtmax(0.1)? .withtolerance(1e-4)? .withinitialconditions(&[1.0])? .withstart(0.0)? .withend(10.0)? .build(); let _solution = solver.solveivp(deriv, &mut ())?; Ok(()) } ```

There is also a solve_ivp function in bacon_sci::ivp that tries a fifth-order predictor-corrector followed by the Runge-Kutta-Fehlberg method followed by BDF6.

Root Finding Algorithms

bacon_sci::roots implements the bisection method, Newton's method, the secant method, Newton's method for polynomials, and Müller's method for polynomials.

As an example, the following code snippet finds the root of x^3 using initial guesses of 0.1 and -0.1.

```rust use bacon_sci::roots::secant; use nalgebra::SVector;

fn cubic(x: &[f64]) -> SVector { SVector::::from_iterator(x.iter.map(|x| x.powi(3))) }

fn solve() -> f64 { secant((&[-0.1], &[0.1]), cubic, 0.001, 1000).unwrap() } ```

Polynomials and Polynomial Interpolation

bacon_sci::polynomial implements a polynomial struct. bacon_sci::interp implements Lagrange interpolation, Hermite interpolation, and cubic spline interpolation.

Scientific Constants

Several scientific constants are defined in bacon_sci::constants. The data comes from NIST. The 2018 CODATA complete listing is available as a hashmap.

Special Functions and Polynomials

Currently, bacon_sci::special allows you to get Legendre polynomials, Hermite polynomials, Laguerre polynomials, and Chebyshev polynomials.

Numeric Differentiation and Quadrature

bacon_sci::differentiate allows first- and second-derivative evaluation numerically. bacon_sci::integrate implements Tanh-Sinh quadrature, adaptive Simpson's rule, Romberg integration, and several adaptive Gaussian integration schemes.