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Numerical (In)Stability of Recurrence Relations
TL;DR
Numerical stability in recurrence relations for Bessel functions varies based on the function type and direction of computation. Understanding these nuances is crucial for accurate calculations.
✦ Why It Matters
Choose the correct direction for applying recurrence relations to ensure numerical stability in your calculations.
Key Takeaways
- Identify the type of Bessel function before applying recurrence relations.
- Use forward computation for Jn and reverse for Yn to maintain stability.
- Implement Miller’s algorithm for stable solutions in numerical computations.
- Monitor rounding errors when dealing with growing and decaying solutions.
How It Works
Recurrence relations for Bessel functions can be stable or unstable depending on the function type and computation direction. For example, Jn is stable in reverse computation, while Yn is not.
This behavior is due to the nature of the solutions, where one may grow and the other decays, leading to numerical errors.