JavaScriptAlgorithm/Maths/MidpointIntegration.js at master · me-hasan/JavaScriptAlgorithm · GitHub

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/**

* @title Midpoint rule for definite integral evaluation

* @author [ggkogkou](https://github.com/ggkogkou)

* @brief Calculate definite integrals with midpoint method

* @details The idea is to split the interval in a number N of intervals and use as interpolation points the xi

* for which it applies that xi = x0 + i*h, where h is a step defined as h = (b-a)/N where a and b are the

* first and last points of the interval of the integration [a, b].

* We create a table of the xi and their corresponding f(xi) values and we evaluate the integral by the formula:

* I = h * {f(x0+h/2) + f(x1+h/2) + ... + f(xN-1+h/2)}

* N must be > 0 and a<b. By increasing N, we also increase precision

* [More info link](https://tutorial.math.lamar.edu/classes/calcii/approximatingdefintegrals.aspx)

function integralEvaluation (N, a, b, func) {

// Check if all restrictions are satisfied for the given N, a, b

if (!Number.isInteger(N) || Number.isNaN(a) || Number.isNaN(b)) { throw new TypeError('Expected integer N and finite a, b') }

if (N <= 0) { throw Error('N has to be >= 2') } // check if N > 0

if (a > b) { throw Error('a must be less or equal than b') } // Check if a < b

if (a === b) return 0 // If a === b integral is zero

// Calculate the step h

const h = (b - a) / N

// Find interpolation points

let xi = a // initialize xi = x0

const pointsArray = []

// Find the sum {f(x0+h/2) + f(x1+h/2) + ... + f(xN-1+h/2)}

let temp

for (let i = 0; i < N; i++) {

temp = func(xi + h / 2)

pointsArray.push(temp)

xi += h

}

// Calculate the integral

let result = h

temp = 0

for (let i = 0; i < pointsArray.length; i++) temp += pointsArray[i]

result *= temp

if (Number.isNaN(result)) { throw Error('Result is NaN. The input interval does not belong to the functions domain') }

return result

}

export { integralEvaluation }

JavaScriptAlgorithm/Maths/MidpointIntegration.js at master · me-hasan/JavaScriptAlgorithm · GitHub

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