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
x22.533.544.5y1.73211.870822.12132.23612.3452

Use linear interpolation in the table to estimate the value x where y = 1.7945.

y = 1.7945
x =
2.Easy
xyx₀ = 1

Apply Newton–Raphson to f(x) = ln x + x − 3 with the starting value x₀ = 1. Find x1.

f(x) = ln x + x − 3f′(x) = 1/x + 1x₀ = 1
x1 =
3.Medium
xy00.3750.751.1251.5

Approximate ∫01.5 sin(x²) dx with the trapezoid rule using n = 4 strips. Give T.

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

The trapezoid rule is used for ∫12 1/x dx. The error is at most (b − a)³·M/(12n²) with M = max|f″| on [1, 2]. Find the smallest number of strips n that guarantees an error below 0.001.

f(x) = 1/x[a, b] = [1, 2]ε = 0.001
n =
5.Hard
00.5111.52ty(0, 2)

Solve y′ = −0.5y, y(0) = 2 with Euler's method and step h = 0.25 up to t = 1.25. The exact solution is y = y₀e−0.5t. Find the global error |E| = |y(1.25) − y5|.

y′ = −0.5yy(0) = 2h = 0.25
|E| =
6.Hard
00.050.10.150.2−1−0.8−0.6ty(0, −1)

Take one step of the classical Runge–Kutta method (RK4) with h = 0.2 for y′ = cos t − y, y(0) = −1. Find y₁ ≈ y(0.2).

y′ = cos t − yy(0) = −1h = 0.2
y1 =

Answer key

  1. 1. x = 2.225
  2. 2. x1 = 2
  3. 3. T = 0.7561
  4. 4. n = 13
  5. 5. |E| = 0.0447
  6. 6. y1 = −0.6387

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