Which of these iterative processes is unstable? (Note: \(\epsilon_n\) is the error in the n^th iteration).(a) \(\frac{\epsilon_{n+1}}{\epsilon_n} = 0.5\)(b) \(\frac{\epsilon_{n+1}}{\epsilon_n} = 0.75\)(c) \(\frac{\epsilon_{n+1}}{\epsilon_n} = 1.25\)(d) \(\frac{\epsilon_{n+1}}{\epsilon_n} = 1\)I got this question in semester exam.I would like to ask this question from Discretization Aspects in chapter Basic Aspects of Discretization, Grid Generation with Appropriate Transformation of Computational Fluid Dynamics

Which of these iterative processes is unstable? (Note: \(\epsilon_n\)

1.	Which of these iterative processes is unstable? (Note: \(\epsilon_n\) is the error in the n^th iteration).(a) \(\frac{\epsilon_{n+1}}{\epsilon_n} = 0.5\)(b) \(\frac{\epsilon_{n+1}}{\epsilon_n} = 0.75\)(c) \(\frac{\epsilon_{n+1}}{\epsilon_n} = 1.25\)(d) \(\frac{\epsilon_{n+1}}{\epsilon_n} = 1\)I got this question in semester exam.I would like to ask this question from Discretization Aspects in chapter Basic Aspects of Discretization, Grid Generation with Appropriate Transformation of Computational Fluid Dynamics
Answer» Correct option is (C) \(\frac{\epsilon_{n+1}}{\epsilon_n} = 1.25\) Explanation: For a SYSTEM to be stable, the error should be decreasing or at least maintained. Representing this MATHEMATICALLY, εn+1 ≤ εn \(\frac{\epsilon_{n+1}}{\epsilon_n} ≤ 1\) For an unstable system, \(\frac{\epsilon_{n+1}}{\epsilon_n} > 1\) This happens in \(\frac{\epsilon_{n+1}}{\epsilon_n} = 1.25\). So, this system is unstable.

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