Home

Solve any problem
(step by step solutions)
Input table (Matrix, Statistics)
Mode :
SolutionHelp
Solution will be displayed step by step (In 2 parts)
Solution
Find Adams bashforth predictor method y'=-2x-y, y(0)=1, x=5

Solution:
Your problem `->` Adams bashforth predictor method y'=-2x-y, y(0)=1, x=5


`y'=-2x-y`

Adam's Bashforth Predictor formula is
`y_(n+1,p) = y_n + h/24 (55y'_(n) - 59y'_(n-1) + 37y'_(n-2) - 9y'_(n-3))`

putting `n=3`, we get

`y_(4,p)=y_3 + h/24 (55y'_(3) - 59y'_2 + 37y'_1 - 9y'_0) ->(2)`

We have given that
`x_0=0,x_1=1.25,x_2=2.5,x_3=3.75`

and using runge kutta 4 method, we get
`y_0=1,y_1=-0.8075,y_2=-3.0945,y_3=-5.5291`

`y'=-2x-y`

`y'_0=-2x-y=-1` (where `x=0,y=1`)

`y'_1=-2x-y=-1.6925` (where `x=1.25,y=-0.8075`)

`y'_2=-2x-y=-1.9055` (where `x=2.5,y=-3.0945`)

`y'_3=-2x-y=-1.9709` (where `x=3.75,y=-5.5291`)

putting the values in (2), we get
`y_(4,p)=y_3 + h/24 (55y'_(3) - 59y'_2 + 37y'_1 - 9y'_0)`

`y_(4,p)=-5.5291 + 1.25/24 * (55 * -1.9709 - 59 * -1.9055 + 37 * -1.6925 - 9 * -1)`

`y_(4,p)=-8.1125`

So, the predicted value is `-8.1125`

Now, we will correct it by corrector method to get the final value





Solution provided by AtoZmath.com
Any wrong solution, solution improvement, feedback then Submit Here
Want to know about AtoZmath.com and me
  
 

Share with your friends
 
Copyright © 2018. All rights reserved. Terms, Privacy