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
xya = 0b = 1

Use the bisection method on f(x) = e−x − x with the starting interval [0, 1]. Find the midpoint c3 of step 3.

f(x) = e−x − x[a, b] = [0, 1]n = 3
c3 =
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
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 =
4.Medium
xy00.250.50.751

Approximate ∫01 √x·e−x dx with Simpson's rule using n = 4 strips. Give S.

f(x) = √x·e−x[a, b] = [0, 1]n = 4
S =
5.Hard
00.20.40.50.60.7ty(0, 0.5)

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

y′ = cos t − yy(0) = 0.5h = 0.5
y1 =
6.Hard
00.20.40.60.51ty(0, 0.5)

Use Heun's method (improved Euler) with h = 0.2 for y′ = 1 + sin(ty), y(0) = 0.5 to estimate y3 ≈ y(0.6).

y′ = 1 + sin(ty)y(0) = 0.5h = 0.2
y3 =

Answer key

  1. 1. c3 = 0.625
  2. 2. x2 = 1.557
  3. 3. S = 1.36
  4. 4. S = 0.3683
  5. 5. y1 = 0.6783
  6. 6. y3 = 1.27

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