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
xyx₀ = 0

Apply Newton–Raphson to f(x) = e−x − x with the starting value x₀ = 0. Find x2.

f(x) = e−x − xf′(x) = −e−x − 1x₀ = 0
x2 =
2.Easy
xyx₀ = 2

Apply Newton–Raphson to f(x) = ln x + x − 2 with the starting value x₀ = 2. Find x2.

f(x) = ln x + x − 2f′(x) = 1/x + 1x₀ = 2
x2 =
3.Medium
xy012

Approximate ∫02 1/(1 + x³) dx with the trapezoid rule using n = 2 strips. Give T.

f(x) = 1/(1 + x³)[a, b] = [0, 2]n = 2
T =
4.Medium
xy00.250.50.751

Approximate ∫01 1/(1 + x³) dx with the trapezoid rule using n = 4 strips. Give T.

f(x) = 1/(1 + x³)[a, b] = [0, 1]n = 4
T =
5.Hard
00.20.40.6−1.4−1.2−1ty(0, −1)

Solve y′ = 0.5y, y(0) = −1 with Euler's method and step h = 0.2 up to t = 0.6. The exact solution is y = y₀e0.5t. Find the global error |E| = |y(0.6) − y3|.

y′ = 0.5yy(0) = −1h = 0.2
|E| =
6.Hard
00.20.411.5ty(0, 1)

Use Euler's method with h = 0.1 for y′ = 1 + sin(ty), y(0) = 1 to estimate y5 ≈ y(0.5).

y′ = 1 + sin(ty)y(0) = 1h = 0.1
y5 =

Answer key

  1. 1. x2 = 0.5663
  2. 2. x2 = 1.557
  3. 3. T = 1.056
  4. 4. T = 0.8317
  5. 5. |E| = 0.01886
  6. 6. y5 = 1.63

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