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/**

* In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order

* numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most

* basic explicit method for numerical integration of ordinary differential equations. The method proceeds in a series

* of steps. At each step the y-value is calculated by evaluating the differential equation at the previous step,

* multiplying the result with the step-size and adding it to the last y-value: y_n+1 = y_n + stepSize * f(x_n, y_n).

*

* (description adapted from https://en.wikipedia.org/wiki/Euler_method)

* @see https://www.geeksforgeeks.org/euler-method-solving-differential-equation/

*/

export function eulerStep(xCurrent, stepSize, yCurrent, differentialEquation) {

// calculates the next y-value based on the current value of x, y and the stepSize

return yCurrent + stepSize * differentialEquation(xCurrent, yCurrent)

}

export function eulerFull(

xStart,

xEnd,

stepSize,

yStart,

differentialEquation

) {

// loops through all the steps until xEnd is reached, adds a point for each step and then returns all the points

const points = [{ x: xStart, y: yStart }]

let yCurrent = yStart

let xCurrent = xStart

while (xCurrent < xEnd) {

// Euler method for next step

yCurrent = eulerStep(xCurrent, stepSize, yCurrent, differentialEquation)

xCurrent += stepSize

points.push({ x: xCurrent, y: yCurrent })

}

return points

}