c) Find y(1.1) and y(1.2) solving y = y – t. Take h = 0.1 and y(1) = d Solve y = et-y taking h = 0.5 given that y(0) = 1 and find two values.

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Can I have a detailed, step-by-step explanation for the part(d) of the following question?

Kindly include the relevant reasoning/assumptions made during simplifications & calculations along with them.

Thank you very much!

 

4. a) Briefly explain (use graphical illustrates as you need), Improved Euler's method.
b) Solve
dy
= y – t2 +1 in the range 0 < t< 0.6 by Improved Euler's method taking
dt
h = 0.2 given that y(0) = 0.5. If the exact solution is y = t2 + 2t +1 – (1/2)et , then
calculate error in each step.
c) Find y(1.1) and y(1.2) solving y = y – t. Take h = 0.1 and y(1) = 2.
d) Solve y = et-y taking h = 0.5 given that y(0) = 1 and find two values.
Transcribed Image Text:4. a) Briefly explain (use graphical illustrates as you need), Improved Euler's method. b) Solve dy = y – t2 +1 in the range 0 < t< 0.6 by Improved Euler's method taking dt h = 0.2 given that y(0) = 0.5. If the exact solution is y = t2 + 2t +1 – (1/2)et , then calculate error in each step. c) Find y(1.1) and y(1.2) solving y = y – t. Take h = 0.1 and y(1) = 2. d) Solve y = et-y taking h = 0.5 given that y(0) = 1 and find two values.
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