Is Simpson's Rule Effective for Solving the Intersecting Cylinders Problem?

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SUMMARY

The discussion centers on the effectiveness of Simpson's (1/3) rule for solving the intersecting cylinders problem. Despite utilizing up to 1,000,000 intervals, users report persistent inaccuracies in the numerical solutions. While the results of numerical integration do converge, they consistently exhibit some degree of error, indicating limitations in Simpson's rule for this specific application.

PREREQUISITES
  • Understanding of numerical integration techniques
  • Familiarity with Simpson's (1/3) rule
  • Knowledge of the intersecting cylinders problem
  • Basic skills in error analysis in numerical methods
NEXT STEPS
  • Research alternative numerical integration methods such as Trapezoidal rule
  • Explore adaptive quadrature techniques for improved accuracy
  • Study error analysis specific to numerical integration
  • Investigate the geometric properties of intersecting cylinders
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Mathematicians, engineers, and researchers working on numerical methods, particularly those focused on geometric problems and integration techniques.

Xishan
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Best numerical technique?

I've recently used Simpson's (1/3) rule for the numerical solution of the 'intersecting cylinders' problem. I've found that it isn't too accurate no matter how many intervals I take (I have even taken 1000,000 intervals!), but still end up with some error.

I'll appreciate anyone for helping me in this matter
 
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What is the intersecting cylinders problem?
 
it is discussed in the thread called 'intersecting cylinders' in this forum. the results of numerical integration do converge but always with some error
 

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