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Created midpoint integration numerical method
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Merge branch 'midpoint_branch' of https://github.com/ggkogkou/Javascr...
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Fixed doxumentation
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,54 @@ | ||
| /** | ||
| * | ||
| * @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) | ||
| * | ||
| */ | ||
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| 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 | ||
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| // Calculate the step h | ||
| const h = (b - a) / N | ||
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| // Find interpolation points | ||
| let xi = a // initialize xi = x0 | ||
| const pointsArray = [] | ||
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| // 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 | ||
| } | ||
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| // Calculate the integral | ||
| let result = h | ||
| temp = 0 | ||
| for (let i = 0; i < pointsArray.length; i++) temp += pointsArray[i] | ||
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| result *= temp | ||
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| if (Number.isNaN(result)) { throw Error('Result is NaN. The input interval does not belong to the functions domain') } | ||
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| return result | ||
| } | ||
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| export { integralEvaluation } |
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| @@ -0,0 +1,16 @@ | ||
| import { integralEvaluation } from '../MidpointIntegration' | ||
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| test('Should return the integral of f(x) = sqrt(x) in [1, 3] to be equal 2.797434', () => { | ||
| const result = integralEvaluation(10000, 1, 3, (x) => { return Math.sqrt(x) }) | ||
| expect(Number(result.toPrecision(6))).toBe(2.79743) | ||
| }) | ||
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| test('Should return the integral of f(x) = sqrt(x) + x^2 in [1, 3] to be equal 11.46410161', () => { | ||
| const result = integralEvaluation(10000, 1, 3, (x) => { return Math.sqrt(x) + Math.pow(x, 2) }) | ||
| expect(Number(result.toPrecision(10))).toBe(11.46410161) | ||
| }) | ||
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| test('Should return the integral of f(x) = log(x) + Pi*x^3 in [5, 12] to be equal 15809.9141543', () => { | ||
| const result = integralEvaluation(20000, 5, 12, (x) => { return Math.log(x) + Math.PI * Math.pow(x, 3) }) | ||
| expect(Number(result.toPrecision(10))).toBe(15809.91415) | ||
| }) |
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