differenting a function over [a,b] using Taylor method

[milkypros]

hi
i am new in fortran programming and i need help on differenting a function over [a,b] using Taylor method. In example the function f(x)=x**3 and i want to calculate the quantity df=(f(x+h)-f(x))/h where h is the (b-a)/n and n is for example 20. Any help?

 

[mikrom]

Post the code, what have you done so far.

 

[milkypros]

Thanks for answering. The code i wrote so far is:

dimension x(0:20)
f(x)=x**3
a=0
b=4
n=20
x(0)=a
x=b
h=(b-a)/n
do i=0,n
x(i)=x(0)+i*h
y=(f(x(i)+h)-f(x(i)))/h
print*,x(i),y
end do
end

I dont know if this is correct. I want to print in one column the x(i) from a to b with increments of h, and in a second column i want to print the coresponting y

 

[mikrom]

I dont know if this is correct.

You should compile and run it and then you would see.

You don't need to use the array x. I would say, something like this does the work:

f(t)[COLOR=#804040][b]=[/b][/color]t[COLOR=#804040][b]**[/b][/color][COLOR=#ff00ff]3[/color]
df(t) [COLOR=#804040][b]=[/b][/color] [COLOR=#ff00ff]3[/color][COLOR=#804040][b]*[/b][/color]t[COLOR=#804040][b]**[/b][/color][COLOR=#ff00ff]2[/color]
a[COLOR=#804040][b]=[/b][/color][COLOR=#ff00ff]0[/color]
b[COLOR=#804040][b]=[/b][/color][COLOR=#ff00ff]4[/color]
n[COLOR=#804040][b]=[/b][/color][COLOR=#ff00ff]20[/color]
h[COLOR=#804040][b]=[/b][/color](b[COLOR=#804040][b]-[/b][/color]a)[COLOR=#804040][b]/[/b][/color]n
x[COLOR=#804040][b]=[/b][/color]a
[COLOR=#804040][b]print[/b][/color] [COLOR=#ff00ff]10[/color], [COLOR=#ff00ff]'x'[/color], [COLOR=#ff00ff]'df_num'[/color], [COLOR=#ff00ff]'df_exact'[/color]
[COLOR=#804040][b]do[/b][/color] i[COLOR=#804040][b]=[/b][/color][COLOR=#ff00ff]0[/color], n
  y[COLOR=#804040][b]=[/b][/color](f(x[COLOR=#804040][b]+[/b][/color]h)[COLOR=#804040][b]-[/b][/color]f(x))[COLOR=#804040][b]/[/b][/color]h
  [COLOR=#804040][b]print[/b][/color] [COLOR=#ff00ff]20[/color], x, y, df(x)
  x[COLOR=#804040][b]=[/b][/color]x[COLOR=#804040][b]+[/b][/color]h
[COLOR=#804040][b]end do[/b][/color]
[COLOR=#6a5acd]10[/color] [COLOR=#804040][b]format[/b][/color] (A4, [COLOR=#008080]3X[/color] , A6, [COLOR=#008080]4X[/color] , A8)
[COLOR=#6a5acd]20[/color] [COLOR=#804040][b]format[/b][/color] ([COLOR=#008080]f4.2[/color], [COLOR=#008080]4X[/color] , [COLOR=#008080]f5.2[/color], [COLOR=#008080]4X[/color] , [COLOR=#008080]f5.2[/color])
[COLOR=#a020f0]end[/color]

Output:

   x   df_num    df_exact
0.00     0.04     0.00
0.20     0.28     0.12
0.40     0.76     0.48
0.60     1.48     1.08
0.80     2.44     1.92
1.00     3.64     3.00
1.20     5.08     4.32
1.40     6.76     5.88
1.60     8.68     7.68
1.80    10.84     9.72
2.00    13.24    12.00
2.20    15.88    14.52
2.40    18.76    17.28
2.60    21.88    20.28
2.80    25.24    23.52
3.00    28.84    27.00
3.20    32.68    30.72
3.40    36.76    34.68
3.60    41.08    38.88
3.80    45.64    43.32
4.00    50.44    48.00

 

[milkypros]

microm
thanks for answering. It works fine. The thing is that when i am trying to set a bigger value of n in order to compare the results, in example n>350, the program doesn't print all the results but it starts from values of x>1,02. whats the problem?

 

[mikrom]

Maybe, because of the settings of your screen buffer.
Redirect the output of the program into a file using >