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he ordinary differential equation dy/dt  = − πy subject to an initial condition y (0) = 1 is solved numerically using the following scheme: 

Where h is the time step, tn =nh , and n = 0, 1, 2, ……. This numerical scheme is stable for all values of h in the interval______. 
  • a)
    For all h > 0
  • b)
    0 < h < 1
  • c)
    0 < h < 2 / π
  • d)
    0 < h < π/ 2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
he ordinary differential equation dy/dt = − πy subject to an ...

−1< (1 − πh) < 1
−2< ( −πh) < 0
2 / π > h > 0
Hence, the correct option is (C) 
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he ordinary differential equation dy/dt = − πy subject to an initial condition y (0) = 1 is solvednumerically using the following scheme:Where h is the time step, tn =nh , and n = 0, 1, 2, ……. This numerical scheme is stable for all values of h in the interval______.a)For all h > 0b)0 < h < 1c)0 < h < 2 / πd)0 < h < π/ 2Correct answer is option 'C'. Can you explain this answer?
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