www.Kelaas.com_Code1, Fortran

www.Kelaas.com_Code1

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Program Blasius_Euler

!Euler Method
Implicit none

integer m,n
real F1,F2,F0,h,i,x,er,c
real, Allocatable :: y(:),y1(:),y2(:)

h=.2
m=int(8.6/h)

Allocate (y(0:m+1),y1(0:m+1),y2(0:m+1))

y(0)=0			!Boundary Condition
y1(0)=0			!Boundary Condition
y2(0)=1			!Initial value for second derivative of y

n=0
er=1

!--------------------------Euler Method-------------------------

do while (er>.001)

do i=0,m

y2(i+1)=y2(i)+h*(-y2(i)*y(i))
	y1(i+1)=y1(i)+h*y2(i)
	y(i+1)=y(i)+h*y1(i)
	x=(i+1)*h

end do

er=abs(y1(m)-1)
y2(0)=y2(0)/y1(m)  ! Interpolating to find second derivative of y 
n=n+1

end do

!--------------------------Euler Method-------------------------

write (*,*) 'Euler Method'
write (*,200) n
200 format ('Number of iterations to find F"(y)=',I3)
write (*,*) ' '
write (*,*) '      eta     ','F(y)     ','F',char(39),'(y)     ','F"(y)   '

do i=0,m
	x=(i+1)*h
	write (*,100) x,y(i+1),y1(i+1),y2(i+1)
	100 format (' ',F9.1,' ',F9.5,' ',F9.5,' ',F9.5)
end do

END Program  Blasius_Euler

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Compilation time: 0.13 sec, absolute running time: 0.07 sec, cpu time: 0.01 sec, memory peak: 3 Mb, absolute service time: 0,28 sec

Euler Method Number of iterations to find F"(y)= 7 eta F(y) F'(y) F"(y) 0.2 0.00000 0.08147 0.40734 0.4 0.01629 0.16294 0.40734 0.6 0.04888 0.24440 0.40601 0.8 0.09776 0.32561 0.40204 1.0 0.16288 0.40602 0.39418 1.2 0.24409 0.48485 0.38134 1.4 0.34106 0.56112 0.36273 1.6 0.45328 0.63367 0.33798 1.8 0.58001 0.70126 0.30734 2.0 0.72027 0.76273 0.27169 2.2 0.87281 0.81707 0.23255 2.4 1.03623 0.86358 0.19196 2.6 1.20894 0.90197 0.15218 2.8 1.38934 0.93241 0.11538 3.0 1.57582 0.95548 0.08332 3.2 1.76692 0.97215 0.05706 3.4 1.96135 0.98356 0.03690 3.6 2.15806 0.99094 0.02242 3.8 2.35625 0.99542 0.01275 4.0 2.55533 0.99797 0.00674 4.2 2.75493 0.99932 0.00329 4.4 2.95479 0.99998 0.00148 4.6 3.15479 1.00028 0.00061 4.8 3.35484 1.00040 0.00022 5.0 3.55492 1.00044 0.00007 5.2 3.75501 1.00046 0.00002 5.4 3.95510 1.00046 0.00001 5.6 4.15519 1.00046 0.00000 5.8 4.35528 1.00046 0.00000 6.0 4.55538 1.00046 0.00000 6.2 4.75547 1.00046 0.00000 6.4 4.95556 1.00046 0.00000 6.6 5.15565 1.00046 0.00000 6.8 5.35574 1.00046 -0.00000 7.0 5.55584 1.00046 0.00000 7.2 5.75593 1.00046 -0.00000 7.4 5.95602 1.00046 0.00000 7.6 6.15611 1.00046 -0.00000 7.8 6.35621 1.00046 0.00000 8.0 6.55630 1.00046 -0.00000 8.2 6.75639 1.00046 0.00000 8.4 6.95648 1.00046 -0.00000 8.6 7.15658 1.00046 0.00000 8.8 7.35667 1.00046 -0.00000