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⇤ ← Revision 1 as of 2010-12-16 11:06:35
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| # Sec 1.9 # Example 3 # Picard iteraction # y'=1+y^2, y(0)=0 |
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| y = function('y',x) y=0 l=[] m=[] sol=function('sol',x) |
y = function('y',x) new_y = function ('new_y',x) p=[] |
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| for i in range(4): sol=x+integral(y**2,x,0,x) y=sol l.append(y) plot(y,x,-3,3) print "y(",i,")=",show(y) |
y = 0 # Initial condition y(0)=0 print 'y( 0 ) is', y for i in range(4): # We calculate 4 iterations new_y = x + integral( y**2 , x , 0 , x ) # By picards Formula, y(n) = x + integral( y(n-1)**2 ) y=new_y print 'y(',i+1,') is', show(y) p.append(plot(y,x,-1,1)) show(sum(p)) |
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| * <Komal>, <Student>, <IT-BHU> | * Aashita Kesarwani, Student, IIT Roorkee * <Your Name>, <Profession>, <Organization> |
Book
Advanced Engineering Mathematics
Author
Erwin Kreyszig
Edition
8th Edition
# Sec 1.9
# Example 3
# Picard iteraction
# y'=1+y^2, y(0)=0
var('x')
y = function('y',x)
new_y = function ('new_y',x)
p=[]
y = 0 # Initial condition y(0)=0
print 'y( 0 ) is', y
for i in range(4): # We calculate 4 iterations
new_y = x + integral( y**2 , x , 0 , x ) # By picards Formula, y(n) = x + integral( y(n-1)**2 )
y=new_y
print 'y(',i+1,') is', show(y)
p.append(plot(y,x,-1,1))
show(sum(p))
Solution by:
- Aashita Kesarwani, Student, IIT Roorkee
<Your Name>, <Profession>, <Organization>