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Calculate Picard Iterates for the IVP y=fx,y,yx0=y0

Description

Calculate an iterative solution to an ODE by using Picard's method.

 

Picard Iterates for the IVP y=fx,y,yx0=y0 

The function fx,y

fx,yx+y2

f:=x,y→x+y2

(1)

Set a=x0  

a0

a:=0

(2)

Set φ0=yx0=y0

φ00

φ0:=0

(3)

Number of iterates

N3

N:=3

(4)

Picard Iterates

for k from 0 to N1 do   φk+1unapplyφ0+∫axft,φktⅆt,x; printnprintfIterate number %d:,k+1 printφk+1x end do:

Iterate number 1:

12x2

Iterate number 2:

12x2+120x5

Iterate number 3:

14400x11+1160x8+120x5+12x2

(5)

 

Commands Used

unapply

See Also

dsolve, for, print


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