Consider the equation= 3t2+ 1with 0 at 0.This is numerically solved by using the forward Euler method with a step size. t = 2. The absolute error in the solution at the end of the first time step is_________Correct answer is '8'. Can you explain this answer?

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Consider the equation

= 3t² + 1 with 0 at 0. This is numerically solved by using the forward Euler method with a step size. ∆t = 2. The absolute error in the solution at the end of the first time step is_________

Correct answer is '8'. Can you explain this answer?

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Consider the equation= 3t2+ 1with 0 at 0.This is numerically solved by...

Approximation value by Euler's Method:

= 3t² + 1 ; u (0) = 0 ; h = Δt = 2
u (2) = u (0) + hf (0, 0) , f (u, t) 3t² + 1
= 0 + 2 (0 + 1) = 2

Exact value:
du = (3t² + 1) dt (var iable separable)
⇒ u = t³ + t + c is sloution
u (0) = (0) ⇒ 0 = c
u = t³ + t
u (2) = 8 + 2 = 10
∴ absolute error

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Consider the equation= 3t2+ 1with 0 at 0.This is numerically solved by using the forward Euler method with a step size. ∆t = 2. The absolute error in the solution at the end of the first time step is_________Correct answer is '8'. Can you explain this answer?

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