2023-10-03 23:08:19 +02:00
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/**
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* In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order
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* numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most
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* basic explicit method for numerical integration of ordinary differential equations. The method proceeds in a series
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* of steps. At each step the y-value is calculated by evaluating the differential equation at the previous step,
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* 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).
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*
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* (description adapted from https://en.wikipedia.org/wiki/Euler_method)
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* @see https://www.geeksforgeeks.org/euler-method-solving-differential-equation/
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*/
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export function eulerStep(xCurrent, stepSize, yCurrent, differentialEquation) {
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// calculates the next y-value based on the current value of x, y and the stepSize
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return yCurrent + stepSize * differentialEquation(xCurrent, yCurrent)
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}
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export function eulerFull(
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xStart,
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xEnd,
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stepSize,
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yStart,
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differentialEquation
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) {
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// loops through all the steps until xEnd is reached, adds a point for each step and then returns all the points
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const points = [{ x: xStart, y: yStart }]
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let yCurrent = yStart
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let xCurrent = xStart
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while (xCurrent < xEnd) {
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// Euler method for next step
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yCurrent = eulerStep(xCurrent, stepSize, yCurrent, differentialEquation)
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xCurrent += stepSize
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points.push({ x: xCurrent, y: yCurrent })
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}
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return points
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}
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