MediumCalculusca-112

Romberg One Step

Problem

Apply one step of Romberg integration to f(x) = sum(coeffs[i] * x^i) on [a, b].

Compute the composite trapezoidal rule with n subintervals (t1) and with 2n subintervals (t2), then return the extrapolated value (4*t2 - t1) / 3. Assume n >= 1.

Hint

Romberg combines two trapezoidal approximations to cancel the leading error term.

Test cases

case 1

in: [[0,0,1],0,2,2]

expected: 2.6666666666666665

case 2

in: [[0,0,0,1],0,1,1]

expected: 0.25

case 3

in: [[1],0,3,1]

expected: 3

case 4

in: [[0,0,0,0,1],0,1,2]

expected: 0.20052083333333334

Starter codePython

def romberg_one_step(coeffs, a, b, n):
    # Your code here
    pass

4 test cases · run your code against them in the editor