blob: 697eba0768d5138a1464697c5d4b065831057826 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
|
//Eg-12.2
//pg-509
clear
clc
x = 0.5;
h = 0.1;
deff('out = func(in)','out = in^2 - sin(in)')
//Forward Difference formulas
f(1) = (func(x+2*h) - 2*func(x+h) + func(x))/h^2;
f(2) = (-func(x+3*h) + 4*func(x+2*h) - 5*func(x+h) + 2*func(x))/(h^2);
//Backward Difference formulas
f(3) = (func(x) - 2*func(x-h) + func(x-2*h))/h^2;
f(4) = (2*func(x)-5*func(x-h)+4*func(x-2*h)-func(x-3*h))/(h^2);
//Central Difference formulas
f(5) = (func(x+h) - 2*func(x) + func(x-h))/(h^2);
f(6) = (-func(x+2*h) + 16*func(x+h) - 30*func(x) + 16*func(x-h) - func(x-2*h))/(12*h^2);
printf('Value of derivative Type Order of error\n')
printf(' %f Forward 1\n',f(1))
printf(' %f Forward 2\n',f(2))
printf(' %f Backward 1\n',f(3))
printf(' %f Backward 2\n',f(4))
printf(' %f Central 2\n',f(5))
printf(' %f Central 4\n\n',f(6))
printf('The exact value is 2.48\nNote that for this function, several formulas in Table 12.2 provide good estimates of second derivate\n')
|
