The question is to use Euler's Method to approximate Y: Y ″ ( t ) = Y ′ ( t ) − 2 Y ( t ) Y ′ ( 0 ) = Y ( 0 ) = 1with t 0 = 0 and h = 0.2So what I did:First iteration: t 1 = 0.2 y ( t 1 ) = y ( t 0 ) + h ⋅ y ′ ( t 0 ) = 1 + 0.2 × 1 = 1.2 y ′ ( t 1 ) = y ′ ( t 0 ) + h ⋅ ( y ′ ( t 0 ) − 2 y ( t 0 ) ) = 1 + 0.2 × ( 1 − 2 × 1 ) = 0.8Second iteration: t 2 = 0.4 y ( t 2 ) = y ( t 1 ) + h ⋅ y ′ ( t 1 ) = 1.2 + 0.2 × 0.8 = 1.36 y ′ ( t 2 ) = y ′ ( t 1 ) + h ⋅ ( y ′ ( t 1 ) − 2 y ( t 1 ) ) = 0.8 + 0.2 × ( 0.8 − 2 × 1.2 ) = − 2.4Correct?

Question

The question is to use Euler&#039;s Method to approximate Y:      Y    ″    (  t  )  =      Y    ′    (  t  )  −  2  Y  (  t  )      Y    ′    (  0  )  =  Y  (  0  )  =  1with       t    0    =  0 and   h  =  0.2So what I did:First iteration:      t    1    =  0.2  y  (      t    1    )  =  y  (      t    0    )  +  h  ⋅      y    ′    (      t    0    )  =  1  +  0.2  ×  1  =  1.2      y    ′    (      t    1    )  =      y    ′    (      t    0    )  +  h  ⋅  (      y    ′    (      t    0    )  −  2  y  (      t    0    )  )  =  1  +  0.2  ×  (  1  −  2  ×  1  )  =  0.8Second iteration:      t    2    =  0.4  y  (      t    2    )  =  y  (      t    1    )  +  h  ⋅      y    ′    (      t    1    )  =  1.2  +  0.2  ×  0.8  =  1.36      y    ′    (      t    2    )  =      y    ′    (      t    1    )  +  h  ⋅  (      y    ′    (      t    1    )  −  2  y  (      t    1    )  )  =  0.8  +  0.2  ×  (  0.8  −  2  ×  1.2  )  =  −  2.4Correct?

Marco Meyer · Accepted Answer

There is an arithmetical mistake at the very last step. I get       y    ′    (      t    2    )  =  0.48.Such problems are easy to code in a spreadsheet.A     B       C0     1       10.2   1.2     0.80.4   1.36    0.480.6   1.456   0.032Here A is for   t, B is for   y  (  t  ), and C is for       y    ′    (  t  ). The top row are initial values A1=0, B1=1, C1=1. The second row is the Euler step: A2=A1+0.2 , B2=B1+0.2*C1, C2=C1+0.2*(C1-2*B1). Then drag down for as many rows as you wish.If for some odd reason you can&#039;t use spreadsheet software during an exam, at least it gives a way to check your hand computations.

Oberhangaps5z · Accepted Answer

I realize this is very old. I think you would first have to transform your second order ODE into two first order ODE&#039;s, then proceed to apply Euler&#039;s method to both equations simultaneously.

The question is to use Euler's Method to approximate Y: Y ″ </msup> (

Answered question

Answer & Explanation

New Questions in Integral Calculus