IA ideas library
Numerical methods IA ideas: iteration, Newton–Raphson, integration and error
Calculators and computers don't solve equations the way you do in class: they iterate. A numerical methods IA asks how an approximation works, how fast it gets close to the answer, and how big the error is. That last question is where the mathematics lives.
The trapezoidal rule (SL) and Euler's method (HL) are in the IB courses; Newton–Raphson, Simpson's rule and fixed-point iteration are not, so explain them as new mathematics. These IAs need no data collection, which suits students who would rather calculate than measure.
Numerical methods & error analysis ideas (8)
- Why does the ancient square-root method double the correct digits?AA SLAA HLSolid
- Trapezoidal rule or Simpson's rule? Areas under the normal curveAA SLAA HLAI SLSolid
- When does Newton–Raphson fail? Cycles, divergence and basins of attractionAA HLAA SLAmbitious
- How small must the step be? Euler's method against an exact solutionAA HLAI HLSolid
- Press cos again and again: when does fixed-point iteration converge?AA SLAA HLSolid
- How many terms do you need? Fast and slow series for πAA HLAmbitious
- What interest rate are you really paying? Solving for the rate by iterationAI SLAI HLAA SLSolid
- When the computer gets it wrong: rounding error and cancellationAA HLAA SLAI HLAmbitious
Also relevant (5)
- How big is my local lake? Estimating area with the trapezoidal ruleAI SLAI HLAA SLAA HLAccessible
- How does a calculator work out sin(x)?AA HLAA SLSolid
- Where should a shared mast go? Minimising total distance to villagesAA HLAI HLAA SLAmbitious
- From steady to chaotic: the logistic map's period doublingAA HLAI HLAmbitious
- How high did the lift go? Integrating a phone's accelerometerAA SLAA HLAI HLSolid
Frequently asked questions
Can a numerical methods IA reach the top of Criterion E?
Yes, if it goes beyond running the method: comparing methods, measuring and explaining the rate at which the error shrinks, and finding cases where a method fails and saying why.
Which numerical methods are in the IB syllabus?
The trapezoidal rule is in both SL courses and Euler's method is in both HL courses. Newton–Raphson, Simpson's rule and the bisection method are not; you may use them if you explain them.
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Related types of IA: Calculus & optimisation · Differential equations & dynamics
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