Limitations of numerical methods
What Limitations of numerical methods means in Mathematics A-Level, as defined for AQA, Pearson Edexcel, WJEC.
Definitions of Limitations of numerical methods
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Reference: AQA
Change of sign methods can fail if f is not continuous, if there is an even number of roots, if the interval is too large, or if the graph touches the axis.
Newton-Raphson fails when f'(xₙ) ≈ 0, since the tangent is near-horizontal and the next iterate is sent far away, or when the iteration cycles or diverges.
Methods can fail through divergence when the derivative of g has magnitude greater than 1 near the root, or when Newton-Raphson iterates cycle.
Factors such as slow convergence, sensitivity to initial guesses, or assumptions in the model that affect a numerical solution.
Drawbacks such as slow convergence, failure near a zero derivative or sensitivity to the starting value.
Topics that use Limitations of numerical methods
- I: Numerical methods (AQA A-Level)
- OT2: Mathematical problem solving (AQA A-Level)
- Overarching theme 2: Mathematical problem solving (Pearson Edexcel A-Level)
- Overarching themes - Mathematical problem solving (WJEC A-Level)
Related terms
- Iterative refinement
- contextual interpretation
- error analysis
- Modelling assumptions
- Multi-step reasoning
- numerical methods
- Trapezium rule
- accuracy and rounding
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