Practice Flashcards
Flip to reveal answersState Euler's method for dy/dx = f(x, y).
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 8 Flashcards — Euler's method
Sign up free to track progress and get spaced-repetition review schedules.
Question
State Euler's method for dy/dx = f(x, y).
Answer
x_(n+1) = x_n + h, y_(n+1) = y_n + h·f(x_n, y_n), where h is the step size.
Question
What does Euler's method actually do geometrically?
Answer
Follows the tangent (gradient f) in small straight steps of length h, approximating the curve by line segments.
Question
Why is Euler's method only an approximation?
Answer
It uses the gradient at the START of each step, so it drifts off a curving solution; error grows with step size h.
Question
If the solution curve is concave up, does Euler over- or under-estimate?
Answer
Underestimate — the tangents lie below a concave-up curve.
Question
If the solution curve is concave down, does Euler over- or under-estimate?
Answer
Overestimate — the tangents lie above a concave-down curve.
Question
How do you find the error of an Euler estimate?
Answer
error = |y_exact − y_Euler|, when the exact solution is known.
Question
What happens to the error if you halve the step size h?
Answer
It roughly halves (error ∝ h), but you need twice as many steps.
Question
Which paper most often features Euler's method?
Answer
Paper 3 (the extended-investigation paper), though it also appears in Paper 2.
Read the notes
Full study notes for Euler's method
Topic 5.18 hub
Differential equations (HL only)
More from Topic 5.18
All flashcards in this topic
Math AA exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free