9. Consider the IVP: y' = (y - cos t) – sint, 0

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9. Consider the IVP: y' = (y - cos t) – sint, 0

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9 Consider The Ivp Y Y Cos T Sint 0 T 3 Y 0 1 5 12 13 2 A Take 1 5000 How Small Do You Need To 1
9 Consider The Ivp Y Y Cos T Sint 0 T 3 Y 0 1 5 12 13 2 A Take 1 5000 How Small Do You Need To 1 (77.23 KiB) Viewed 29 times
9. Consider the IVP: y' = (y - cos t) – sint, 0<t<3 y(0) = 1.5. (12) (13) 2 (a) Take 1 = -5000. How small do you need to take At in the forward Euler method to obtain a stable and accurate approximation to the solution of (12)-(13). Ex- plain. (b) Compute and plot the numerical approximation in (a). Explain the result. (c) Consider the backward Euler and the implicit) trapezoidal rule method applied to the IVP (12)-(13). Taking At = 0.2, 0.1 compare (by plotting) the corresponding numerical approximations. Explain why the first order method produces more accurate results than the second order method.
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