Numerical methods worksheet with answers

Free printable Numerical methods worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
x22.22.42.62.83y1.38631.43511.48161.52611.56861.6094

Use linear interpolation in the table to estimate y at x = 2.52.

x = 2.52
y =
2.Easy
xya = 0b = 1

Use the bisection method on f(x) = cos x − x with the starting interval [0, 1]. Find the midpoint c4 of step 4.

f(x) = cos x − x[a, b] = [0, 1]n = 4
c4 =
3.Medium
xy00.250.50.751

Approximate ∫01 1/(1 + x³) dx with Simpson's rule using n = 4 strips. Give S.

f(x) = 1/(1 + x³)[a, b] = [0, 1]n = 4
S =
4.Medium
xy00.511.52

Approximate ∫02 1/√(1 + x⁴) dx with Simpson's rule using n = 4 strips. Give S.

f(x) = 1/√(1 + x⁴)[a, b] = [0, 2]n = 4
S =
5.Hard
00.20.40.60.80.40.5ty(0, 0.5)

Solve y′ = t − y, y(0) = 0.5 with Euler's method and step h = 0.2 up to t = 0.8. The exact solution is y = t − 1 + (y₀ + 1)e−t. Find the global error |E| = |y(0.8) − y4|.

y′ = t − yy(0) = 0.5h = 0.2
|E| =
6.Hard
00.050.10.150.22.62.83ty(0, 3)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.2 for y′ = cos t − y, y(0) = 3. Find y₁ ≈ y(0.2).

y′ = cos t − yy(0) = 3h = 0.2
y1 =

Answer key

  1. 1. y = 1.508
  2. 2. c4 = 0.6875
  3. 3. S = 0.8358
  4. 4. S = 1.36
  5. 5. |E| = 0.05959
  6. 6. y1 = 2.636

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