Use Euler's method to find approximate values for the solution of the initial value − problem d y d x = x − y y ( 0 ) = 1on the interval [0,1] using five steps of size h=0.2.My attempts:I know that the recurrence relation y n + 1 = y n + h f ( x n , y n ) however I am unable to see how the interval comes into play.An idea I had was to consider the bounds of the interval and approximate y(0) and y(1) however this does not include h so I am extremely skeptical.

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Use Euler&#039;s method to find approximate values for the solution of the initial value − problem            d      y              d      x        =  x  −  y  y  (  0  )  =  1on the interval [0,1] using five steps of size h=0.2.My attempts:I know that the recurrence relation       y          n      +      1        =      y          n        +  h  f  (      x    n    ,      y    n    ) however I am unable to see how the interval comes into play.An idea I had was to consider the bounds of the interval and approximate y(0) and y(1) however this does not include h so I am extremely skeptical.

ticotaku86 · Accepted Answer

Make a little table -- I&#039;ve filled in the first couple of rows for you:                    x                    y                    Δ        x                                          d            y                                d            x                          =        x        −        y                    Δ        y        ≈                              d            y                                d            x                          Δ        x                            0                    1                    0.2                    −        1                    −        0.2                            0.2                    0.8                    0.2                    −        0.6                    −        0.12                            0.4                    0.68                    0.2                                        0.6                          0.2                                        0.8                          0.2                                        1                          0.2                        You are done when you get to the bottom left.

Wevybrearttexcl · Accepted Answer

You compute step-by-step approximations of   y  (  0.2  ),   y  (  0.4  ),   y  (  0.6  ),   y  (  0.8  ) and then   y  (  1.0  ). Or in other words,       x    n    =      x    0    +  n  ⋅  h and       y    n   is the approximation of   y  (      x    n    ).

Use Euler's method to find approximate values for the solution of the initial value − problem dy/dx=x−y (0)=1 on the interval [0,1] using five steps of size h=0.2.

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