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
44
|
clc
clear
x=[0 0.2 0.4 0.6 0.8]
h=0.2
y(1,1)=-1
for i=1:4
k1(1,i)=h*(-2*x(1,i)-y(1,i))
k2(1,i)=h*(-2*(x(1,i)+h/4)-(y(1,i)+k1(1,i)/4))
k3(1,i)=h*(-2*(x(1,i)+(3*h)/8)-(y(1,i)+(3*k1(1,i))/32+(9*k2(1,i))/32))
k4(1,i)=h*(-2*(x(1,i)+(12*h)/13)-(y(1,i)+(1932*k1(1,i))/2197-(7200*k2(1,i))/2197+(7296*k3(1,i))/2197))
k5(1,i)=h*(-2*(x(1,i)+(h))-(y(1,i)+(439*k1(1,i))/216-(8*k2(1,i))+(3680*k3(1,i))/513-(845*k4(1,i)/4104)))
k6(1,i)=h*(-2*(x(1,i)+(h/2))-(y(1,i)-(8*k1(1,i))/27+(2*k2(1,i))-(3544*k3(1,i))/2565+(1859*k4(1,i)/4104)-11*k5(1,i)/40))
kA(1,i)=(16*k1(1,i)/135+6656*k3(1,i)/12825+28561*k4(1,i)/56430-9*k5(1,i)/50+2*k6(1,i)/55)
y(1,i+1)=y(1,i)+kA(1,i)
B(1,i)=-3.*exp(-x(1,i))-2*x(1,i)+2
C(1,i)=-2*x(1,i)-y(1,i)
end
for i=1:3
T=[x(1,i), y(1,i),B(1,i) ,C(1,i)]
disp(T)
end
P=y(1,3)+(h/12)*(23*C(1,3)-16*C(1,2)+5*C(1,1))
printf('Value at y(0.6) is %f',P)
x=[0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8]
h=0.1
y(1,1)=-1
for i=1:7
k1(1,i)=h*(-2*x(1,i)-y(1,i))
k2(1,i)=h*(-2*(x(1,i)+h/4)-(y(1,i)+k1(1,i)/4))
k3(1,i)=h*(-2*(x(1,i)+(3*h)/8)-(y(1,i)+(3*k1(1,i))/32+(9*k2(1,i))/32))
k4(1,i)=h*(-2*(x(1,i)+(12*h)/13)-(y(1,i)+(1932*k1(1,i))/2197-(7200*k2(1,i))/2197+(7296*k3(1,i))/2197))
k5(1,i)=h*(-2*(x(1,i)+(h))-(y(1,i)+(439*k1(1,i))/216-(8*k2(1,i))+(3680*k3(1,i))/513-(845*k4(1,i)/4104)))
k6(1,i)=h*(-2*(x(1,i)+(h/2))-(y(1,i)-(8*k1(1,i))/27+(2*k2(1,i))-(3544*k3(1,i))/2565+(1859*k4(1,i)/4104)-11*k5(1,i)/40))
kA(1,i)=(16*k1(1,i)/135+6656*k3(1,i)/12825+28561*k4(1,i)/56430-9*k5(1,i)/50+2*k6(1,i)/55)
y(1,i+1)=y(1,i)+kA(1,i)
B(1,i)=-3.*exp(-x(1,i))-2*x(1,i)+2
C(1,i)=-2*x(1,i)-y(1,i)
end
for i=1:6
T=[x(1,i), y(1,i),B(1,i) ,C(1,i)]
disp(T)
end
R=y(1,6)+(h/12)*(23*C(1,6)-16*C(1,5)+5*C(1,4))
printf('Value at y(0.6) is %f',)
|
