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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Name: ____________________   Date: ____________

1.Easy
x22.533.544.5y1.73211.870822.12132.23612.3452

Use linear interpolation in the table to estimate y at x = 3.875.

x = 3.875
y =
2.Easy
xyx₀ = 0.5

Apply Newton–Raphson to f(x) = e−x − x with the starting value x₀ = 0.5. Find x2.

f(x) = e−x − xf′(x) = −e−x − 1x₀ = 0.5
x2 =
3.Medium
xy00.51

Approximate ∫01 sin(x²) dx with the trapezoid rule using n = 2 strips. Give T.

f(x) = sin(x²)[a, b] = [0, 1]n = 2
T =
4.Medium
xy00.33330.66671

Approximate ∫01 1/(1 + x³) dx with the trapezoid rule using n = 3 strips. Give T.

f(x) = 1/(1 + x³)[a, b] = [0, 1]n = 3
T =
5.Hard
00.511.50.511.52ty(0, 0.5)

Solve y′ = y(2 − y), y(0) = 0.5 with Euler's method and step h = 0.5 up to t = 1.5. The exact solution is y = 2y₀/(y₀ + (2 − y₀)e−2t). Find the global error |E| = |y(1.5) − y3|.

y′ = y(2 − y)y(0) = 0.5h = 0.5
|E| =
6.Hard
00.050.10.150.20.50.550.6ty(0, 0.5)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.2 for y′ = cos t − y, y(0) = 0.5. Find y₁ ≈ y(0.2).

y′ = cos t − yy(0) = 0.5h = 0.2
y1 =

Answer key

  1. 1. y = 2.207
  2. 2. x2 = 0.5671
  3. 3. T = 0.3341
  4. 4. T = 0.8286
  5. 5. |E| = 0.05968
  6. 6. y1 = 0.5894

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