### 1 unstable release

0.11.0 | Aug 26, 2021 |
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#**4** in #quadrature

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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

using the Runge-Kutta-Fehlberg
method.`y ' = y`

`use` `bacon_sci``::``ivp``::``{``RK45``,` RungeKuttaSolver`}``;`
`use` `nalgebra``::``{`VectorN`,` `U1``}``;`
`fn` `deriv``(``_t``:` `f64`, `y``:` `&`[`f64`], `_params``:` `&``mut` `(``)``)`` ``->` `Result``<`VectorN`<``f64`, U1`>`, `String``>` `{`
`Ok``(``VectorN``::``<``f64`, U1`>``::`from_column_slice`(`y`)``)`
`}`
`fn` `solve``(``)`` ``->` `Result``<``(``)`, `String``>` `{`
`let` solver `=` `RK45``::`new`(``)`
`.``with_dt_min``(``0.``01``)``?`
`.``with_dt_max``(``0.``1``)``?`
`.``with_tolerance``(`1e`-``4``)``?`
`.``with_initial_conditions``(``&``[``1.``0``]``)``?`
`.``with_start``(``0.``0``)``?`
`.``with_end``(``10.``0``)``?`
`.``build``(``)``;`
`let` _solution `=` solver`.``solve_ivp``(`deriv`,` `&``mut` `(``)``)``?``;`
`Ok``(``(``)``)`
`}`

There is also a

function in `solve_ivp`

that tries a fifth-order
predictor-corrector followed by the Runge-Kutta-Fehlberg method followed by
BDF6.`bacon_sci ::`ivp

# Root Finding Algorithms

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

As an example, the following code snippet finds the root of

using
initial guesses of `x ^3`

`0.``1`

and `-``0.``1`

.`use` `bacon_sci``::``roots``::`secant`;`
`use` `nalgebra``::``{`VectorN`,` `U1``}``;`
`fn` `cubic``(``x``:` `&`[`f64`]`)`` ``->` `VectorN``<``f64`, U1`>` `{`
`VectorN``::``<``f64`, U1`>``::`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

implements a polynomial struct. `bacon_sci ::`polynomial

`bacon_sci``::`interp

implements
Lagrange interpolation, Hermite interpolation, and cubic spline interpolation.# Scientific Constants

Several scientific constants are defined in

. The data
comes from NIST. The 2018 CODATA complete listing is available as a hashmap.`bacon_sci ::`constants

# Special Functions and Polynomials

Currently,

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

# Numeric Differentiation and Quadrature

allows first- and second-derivative evaluation numerically.
`bacon_sci ::`differentiate

`bacon_sci``::`integrate

implements Tanh-Sinh quadrature, adaptive Simpson's rule,
Romberg integration, and several adaptive Gaussian integration schemes.#### Dependencies

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