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
37
38
39
40
41
42
43
|
//Eg-13.6
//pg-533
clear
clc
//Equation [27] is used for computation.
deff('out = func(in1,in2)','out = in2-in1')
h = 0.1;
y(1) = 0;
//The given equation dy/dx = y-x is of the form dy/dx + Py = Q
// Finally the analytical expression is y = x-exp(x) + 1
//The index starts from 1 and goes up to 11 instead of 0 to 10
for(i = 1:11)
x(i) = 0 + (i-1)*h;
z(i) = x(i) - exp(x(i)) + 1;
end
a = (2^0.5-1)/2;
b = (2-2^0.5)/2;
c = -(2^0.5)/2;
d = 1 + (2^0.5)/2;
printf('i x(i) y(i) k1 k2 k3 k4 y(i+1) y(i+1)Exact\n')
for(i = 1:10)
k1(i) = h*func(x(i),y(i));
k2(i) = h*func(x(i)+h/2,y(i)+k1(i)/2);
k3(i) = h*func(x(i)+h/2,y(i)+a*k1(i)+b*k2(i));
k4(i) = h*func(x(i)+h,y(i)+c*k2(i)+d*k3(i));
y(i+1) = y(i) + 1/6*(k1(i)+2*b*k2(i)+2*d*k3(i)+k4(i));
printf(' %d %f %f %f %f %f %f %f %f\n',i,x(i),y(i),k1(i),k2(i),k3(i),k4(i),y(i+1),z(i+1))
end
printf(' 11 %f %f\n',x(i+1),y(i+1))
printf('\n Therefore, y(1) = %f\n',y(i+1))
printf('\n Refer to the textbook for the analytical solution\n')
|
