| 1 | # RungeKuttaJS
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| 2 |
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| 3 | > JavaScript implementation of the classic Runge-Kutta method (RK4)
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| 4 |
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| 5 | [![npm][npm-badge]][npm-url] [![build][build-badge]][build-url] [![coverage][coverage-badge]][coverage-url] [![Known Vulnerabilities][vulnerabilities-badge]][vulnerabilities-url] [![dependencies][dependencies-badge]][dependencies-url] [![size][size-badge]][size-url] [![types][types-badge]][types-url] [![unicorn][unicorn-badge]][unicorn-url] [![xo][xo-badge]][xo-url] [![license][license-badge]][license-url]
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| 6 |
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| 7 | ## Key notes / highlights
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| 8 |
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| 9 | - Solves ordinary diffenrential equations numerically
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| 10 | - Less error prone than a Euler integration
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| 11 | - Works with single equations and systems of equations
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| 12 | - Minimal implementation
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| 13 |
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| 14 | ## Install
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| 15 |
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| 16 | ```console
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| 17 | $ npm install runge-kutta
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| 18 | ```
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| 19 |
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| 20 | ## Usage
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| 21 |
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| 22 | Suppose you want to predict the spread of a viral disease. The SIR model could be implemented and solved with the following four lines of code.
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| 23 |
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| 24 | ```js
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| 25 | import rungeKutta from 'runge-kutta';
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| 26 |
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| 27 | // Setup parameters for the transmission speed (T)
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| 28 | // and the recovery rate R (R).
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| 29 | // This corresponds to a basic reproduction number equal to 3
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| 30 | // ~ T/R.
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| 31 | const T = .2143, R = 1/14;
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| 32 | // Define the set of ordinary differential equations.
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| 33 | const dSIR = (t, y) => [-T * y[0] * y[1], (T * y[0] - R) * y[1], R * y[1]];
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| 34 |
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| 35 | // Solve the system and log the result (reduced to the infection count).
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| 36 | console.log(rungeKutta(dSIR, [1, .1, 0], [0, 14], .2).map(x => x[1]));
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| 37 | ```
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| 38 |
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| 39 | ## API
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| 40 |
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| 41 | ### Methods
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| 42 |
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| 43 | #### rungeKutta
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| 44 |
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| 45 | ► **rungeKutta**(`ODE`: initialValueFunction, `initialCondition`: number | number[], `range`: readonly [number, number], `stepSize` = 1): number[] | number[][]
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| 46 |
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| 47 | Solves the the initial value problem given through `ODE`. It is specified through a function taking in a number for the undependent variable and a number or an array of numbers for the dependent variable(s):
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| 48 |
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| 49 | ```js
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| 50 | type initialValueFunction = (x: number, y: any) => any;
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| 51 | type initialValueFunctionSingle = (x: number, y: number) => number;
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| 52 | type initialValueFunctionMulti = (x: number, y: readonly number[]) => number[];
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| 53 | ```
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| 54 |
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| 55 | If the `initialCondition` is a number (or an array containg one number) the `rungeKutta` assumes a single variable problem, otherwise a multi variable problem.
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| 56 |
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| 57 | ##### Example (Single variable problem: y' = y, y(0) = 1)
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| 58 |
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| 59 | ```js
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| 60 | const dy = (t, y) => y;
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| 61 | const approxExp = rungeKutta(dy, 1, [0, 8], .1);
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| 62 | console.log(approxExp);
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| 63 | ```
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| 64 |
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| 65 | A multi variable problem is given in the introduction.
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| 66 |
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| 67 | ## Keywords
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| 68 |
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| 69 | - math
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| 70 | - mathematics
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| 71 | - numerical
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| 72 | - numeric
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| 73 | - methods
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| 74 | - solve
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| 75 | - differential
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| 76 | - equation
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| 77 | - system
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| 78 | - equations
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| 79 | - calculus
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| 80 |
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| 81 | ## Dependencies
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| 82 |
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| 83 | - [type-insurance](https://www.npmjs.com/package/type-insurance)
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| 84 |
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| 85 | ## Related
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| 86 |
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| 87 | - [nsolvejs](https://www.npmjs.com/package/nsolvejs) - Solve equations numerically and regression analysis
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| 88 |
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| 89 | ## Maintainer
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| 90 |
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| 91 | - [Ruben Giannotti](http://rubengiannotti.com) - ruben.giannotti@gmx.net - github.com/giannotr
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| 92 |
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| 93 | [npm-badge]: https://img.shields.io/npm/v/runge-kutta.svg
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| 94 | [npm-url]: https://www.npmjs.com/package/runge-kutta
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| 95 | [build-badge]: https://travis-ci.org/giannotr/runge-kutta-js.svg?branch=master
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| 96 | [build-url]: https://travis-ci.org/giannotr/runge-kutta-js
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| 97 | [coverage-badge]: https://coveralls.io/repos/github/giannotr/runge-kutta-js/badge.svg?branch=master
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| 98 | [coverage-url]: https://coveralls.io/github/giannotr/runge-kutta-js?branch=master
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| 99 | [vulnerabilities-badge]: https://snyk.io/test/github/giannotr/runge-kutta-js/badge.svg?targetFile=package.json
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| 100 | [vulnerabilities-url]: https://snyk.io/test/github/giannotr/runge-kutta-js?targetFile=package.json
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| 101 | [dependencies-badge]: https://david-dm.org/giannotr/runge-kutta-js.svg
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| 102 | [dependencies-url]: https://david-dm.org/giannotr/runge-kutta-js
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| 103 | [size-badge]: https://badgen.net/packagephobia/publish/runge-kutta
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| 104 | [size-url]: https://packagephobia.now.sh/result?p=runge-kutta
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| 105 | [types-badge]: https://badgen.net/npm/types/runge-kutta
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| 106 | [types-url]: https://github.com/giannotr/runge-kutta-js/tree/master/src
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| 107 | [unicorn-badge]: https://img.shields.io/badge/unicorn-approved-ff69b4.svg
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| 108 | [unicorn-url]: https://www.youtube.com/watch?v=9auOCbH5Ns4
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| 109 | [xo-badge]: https://img.shields.io/badge/code_style-XO-5ed9c7.svg
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| 110 | [xo-url]: https://github.com/xojs/xo
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| 111 | [license-badge]: https://img.shields.io/github/license/giannotr/runge-kutta-js.svg
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| 112 | [license-url]: https://github.com/giannotr/runge-kutta-js/blob/master/LICENSE
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