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 4. Every step halves the interval. How many steps n are needed at least before the interval is shorter than 0.005?

b − a = 4ε = 0.005
n =
2.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 0.01?

b − a = 1ε = 0.01
n =
3.Medium
xy00.30.60.91.21.5

Approximate ∫01.5 sin(x²) dx with the trapezoid rule using n = 5 strips. Give T.

f(x) = sin(x²)[a, b] = [0, 1.5]n = 5
T =
4.Medium
xy12.54

Approximate ∫14 1/x dx with Simpson's rule, n = 2, and compare it with the exact value. Find the absolute error |E| = |S − I|.

f(x) = 1/x[a, b] = [1, 4]n = 2
|E| =
5.Hard
00.20.41.61.82ty(0, 2)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.5 for y′ = cos t − y, y(0) = 2. Find y₁ ≈ y(0.5).

y′ = cos t − yy(0) = 2h = 0.5
y1 =
6.Hard
00.050.10.50.550.6ty(0, 0.5)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.1 for y′ = 1 + sin(ty), y(0) = 0.5. Find y₁ ≈ y(0.1).

y′ = 1 + sin(ty)y(0) = 0.5h = 0.1
y1 =

Answer key

  1. 1. n = 10
  2. 2. n = 7
  3. 3. T = 0.7641
  4. 4. |E| = 0.03871
  5. 5. y1 = 1.588
  6. 6. y1 = 0.6028

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