Finding solution of differential equation using euler numerical method d y d x = 0.3 y − 10 and 0 ≤ x ≤ 3 and x = 0 , y = 40.What i have tried y n = y n − 1 + h ⋅ f ( x n − 1 , y n − 1 ) Where f ( x , y ) = 0.3 y − 10.I have a doubt that what should i take width interval h in above question.(which is not mention here)Can anyone please explain me what i take value of h. Thanks

Question

Finding solution of differential equation using euler numerical method                     d        y                    d        x              =    0.3    y    −    10   and   0  ≤  x  ≤  3 and   x  =  0  ,  y  =  40.What i have tried            y              n              =          y              n        −        1              +    h    ⋅    f    (          x              n        −        1              ,          y              n        −        1              )  Where   f  (  x  ,  y  )  =  0.3  y  −  10.I have a doubt that what should i take width interval   h in above question.(which is not mention here)Can anyone please explain me what i take value of   h. Thanks

Ragazzonibw · Accepted Answer

You just wrote the euler algorithm. Notice that   f  (      x    n    ,      y    n    )  =  0.3      y    n    −  10. Thus,      y    n    =      y          n      −      1        +  h  (  0.3      y          n      −      1        −  10  )  =  (  1  +  0.3  h  )      y          n      −      1        −  10  hNow, since you are not given   h, you may pick for instance   h  =  1, for simplicity. Then, you have an algorithm:      {                                        y            n                    =          1.3                      y                          n              −              1                                −          10                                                  x            0                    =          0                                                  y            0                    =          40

Finding solution of differential equation using euler numerical method dy/dx=0.3y−10 and 0<=x<=3 and x=0,y=40.

Answered question

Answer & Explanation

New Questions in Integral Calculus