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

The bisection method starts on an interval of length 1. Every step halves the interval. How many steps n are needed at least before the interval is shorter than 0.0002?

b − a = 1ε = 0.0002
n =
2.Easy
xya = 0b = 1

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

f(x) = e−x − x[a, b] = [0, 1]n = 4
c4 =
3.Medium
xy00.51

Approximate ∫01 x³ dx with the trapezoid rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |T − I|.

f(x) = x³[a, b] = [0, 1]n = 2
|E| =
4.Medium
t (s)010203040v (m/s)712172019

A vehicle's speed is measured every 10 s (table). Estimate the distance s travelled from t = 0 to t = 40 s with the trapezoid rule.

h = 10 sn = 4
s = m
5.Hard
00.20.40.60.51ty(0, 0.5)

Use Heun's method (improved Euler) with h = 0.25 for y′ = e−ty, y(0) = 0.5 to estimate y3 ≈ y(0.75).

y′ = e−tyy(0) = 0.5h = 0.25
y3 =
6.Hard
00.10.20.311.11.21.3ty(0, 1)

Use Heun's method (improved Euler) with h = 0.1 for y′ = e−ty, y(0) = 1 to estimate y3 ≈ y(0.3).

y′ = e−tyy(0) = 1h = 0.1
y3 =

Answer key

  1. 1. n = 13
  2. 2. c4 = 0.5625
  3. 3. |E| = 0.0625
  4. 4. s = 620 m
  5. 5. y3 = 1.046
  6. 6. y3 = 1.253

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