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%clear;
clc;
format long g
tic
%bagian n=10
syms c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 t r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
c0=0; c1=1/10; c2=2/10; c3=3/10; c4=4/10; c5=5/10; c6=6/10; c7=7/10; c8=8/10; c9=9/10; c10=10/10; r0=0; r1=1; r2=2; r3=3; r4=4; r5=5; r6=6; r7=7; r8=8; r9=9; r10=10;
EvalAt = [c0, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10];
ktemp = arrayfun(@(EA) euler([r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10], EA).', EvalAt, 'uniform', 0);
ptemp=arrayfun(@(EA) int((t)*euler([r0, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10],t),t,0,EA).', EvalAt, 'uniform', 0);
E = horzcat(ktemp{:}).'
K = horzcat(ptemp{:}).'
Ek=E-K
Inv_Ek= inv(Ek) ;
F=[1-c0*(sin(c0)-cos(c0));1-c1*(sin(c1)-cos(c1));1-c2*(sin(c2)-cos(c2));1-c3*(sin(c3)-cos(c3));1-c4*(sin(c4)-cos(c4));1-c5*(sin(c5)-cos(c5));1-c6*(sin(c6)-cos(c6));1-c7*(sin(c7)-cos(c7));1-c8*(sin(c8)-cos(c8));1-c9*(sin(c9)-cos(c9));1-c10*(sin(c10)-cos(c10))]
C=Ek\F
%solusi aproximasinya
Ua=@(x)(C(1)*euler(0,x)+C(2)*euler(1,x)+C(3)*euler(2,x)+C(4)*euler(3,x)+C(5)*euler(4,x)+C(6)*euler(5,x)+C(7)*euler(6,x)+C(8)*euler(7,x)+C(9)*euler(8,x)+C(10)*euler(9,x)+C(11)*euler(10,x)) ;
Ue=@(x)(sin(x)+cos(x)) ;
uaa=zeros(11,1) ;
uee=zeros(11,1) ;
xx=zeros(11,1) ;
k=0;
for i=1:11
uaa(i)=Ua(k);
uee(i)=Ue(k);
xx(i)=k;
k=k+.1;
end
Uap= uaa;
Uex= uee;
y=(abs(uaa-uee));
[xx uee uaa y];
uee
uaa
y
%bagian n=6
syms s0 s1 s2 s3 s4 s5 s6 t r0 r1 r2 r3 r4 r5 r6
s0=0/6; s1=1/6; s2=2/6; s3=3/6; s4=4/6; s5=5/6; s6=6/6; r0=0; r1=1; r2=2; r3=3; r4=4; r5=5; r6=6;
EvalAt = [s0, s1, s2, s3, s4, s5, s6];
ktemp = arrayfun(@(EA) euler([r0, r1, r2, r3, r4, r5, r6], EA).', EvalAt, 'uniform', 0);
ptemp=arrayfun(@(EA) int((t)*euler([r0, r1, r2, r3, r4, r5, r6],t),t,0,EA).', EvalAt, 'uniform', 0);
E2 = horzcat(ktemp{:}).'
K2 = horzcat(ptemp{:}).'
Ek2=E2-K2
Inv_Ek2= inv(Ek2) ;
F2=[1-s0*(sin(s0)-cos(s0));1-s1*(sin(s1)-cos(s1));1-s2*(sin(s2)-cos(s2));1-s3*(sin(s3)-cos(s3));1-s4*(sin(s4)-cos(s4));1-s5*(sin(s5)-cos(s5));1-s6*(sin(s6)-cos(s6))]
C2=Ek2\F2
%solusi aproximasinya
Ua2=@(x)(C2(1)*euler(0,x)+C2(2)*euler(1,x)+C2(3)*euler(2,x)+C2(4)*euler(3,x)+C2(5)*euler(4,x)+C2(6)*euler(5,x)+C2(7)*euler(6,x)) ;
Ue=@(x)(sin(x)+cos(x)) ;
uaa2=zeros(11,1) ;
uee=zeros(11,1) ;
xx=zeros(11,1) ;
k=0;
for i=1:11
uaa2(i)=Ua2(k);
uee(i)=Ue(k);
xx(i)=k;
k=k+.1;
end
Uap2= uaa2;
Uex= uee;
y2=(abs(uaa2-uee));
[xx uee uaa2 y2];
uee
uaa2
y2
%bagian n=2
syms w0 w1 w2 t r0 r1 r2
w0=0/2; w1=1/2; w2=2/2; r0=0; r1=1; r2=2;
EvalAt = [w0, w1, w2];
ktemp = arrayfun(@(EA) euler([r0, r1, r2], EA).', EvalAt, 'uniform', 0);
ptemp=arrayfun(@(EA) int((t)*euler([r0, r1, r2],t),t,0,EA).', EvalAt, 'uniform', 0);
E3 = horzcat(ktemp{:}).'
K3 = horzcat(ptemp{:}).'
Ek3=E3-K3
Inv_Ek3= inv(Ek3) ;
F3=[1-w0*(sin(w0)-cos(w0));1-w1*(sin(w1)-cos(w1));1-w2*(sin(w2)-cos(w2))]
C3=Ek3\F3
%solusi aproximasinya
Ua3=@(x)(C3(1)*euler(0,x)+C3(2)*euler(1,x)+C3(3)*euler(2,x)) ;
Ue=@(x)(sin(x)+cos(x)) ;
uaa3=zeros(11,1) ;
uee=zeros(11,1) ;
xx=zeros(11,1) ;
k=0;
for i=1:11
uaa3(i)=Ua3(k);
uee(i)=Ue(k);
xx(i)=k;
k=k+.1;
end
Uap3= uaa3;
Uex= uee;
y3=(abs(uaa3-uee));
[xx uee uaa3 y3];
uee
uaa3
y3
%gambar
plot(xx,uee,'k',xx,uaa,'o',xx,uaa2,'c*',xx,uaa3,'--')
grid on
legend({'eksak','aproksimasi N=10','aproksimasi N=6','aproksimasi N=2'},'Location','Northwest')
plot(xx,y)
title('Error N=10')
plot(xx,y2)
title('Error N=6')
plot(xx,y3)
title('Error N=2')
grid on
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