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format long e
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%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=0.1; c2=0.2; c3=0.3; c4=0.4; c5=0.5; c6=0.6; c7=0.7; c8=0.8; c9=0.9; c10=1; 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(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;1+c1;1+c2;1+c3;1+c4;1+c5;1+c6;1+c7;1+c8;1+c9;1+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)(2*exp(x)-1) ;
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=8
syms s0 s1 s2 s3 s4 s5 s6 s7 s8 t r0 r1 r2 r3 r4 r5 r6 r7 r8
s0=0/8; s1=1/8; s2=2/8; s3=3/8; s4=4/8; s5=5/8; s6=6/8; s7=7/8; s8=8/8; r0=0; r1=1; r2=2; r3=3; r4=4; r5=5; r6=6; r7=7; r8=8;
EvalAt = [s0, s1, s2, s3, s4, s5, s6, s7, s8];
ktemp = arrayfun(@(EA) euler([r0, r1, r2, r3, r4, r5, r6, r7, r8], EA).', EvalAt, 'uniform', 0);
ptemp=arrayfun(@(EA) int(euler([r0, r1, r2, r3, r4, r5, r6, r7, r8],t),t,0,EA).', EvalAt, 'uniform', 0);
E2 = horzcat(ktemp{:}).' ;
K2 = horzcat(ptemp{:}).' ;
Ek2=E2-K2 ;
Inv_Ek= inv(Ek2) ;
F2=[1+s0;1+s1;1+s2;1+s3;1+s4;1+s5;1+s6;1+s7;1+s8];
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)+C2(8)*euler(7,x)+C2(9)*euler(8,x)) ;
Ue=@(x)(2*exp(x)-1) ;
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(euler([r0, r1, r2],t),t,0,EA).', EvalAt, 'uniform', 0);
E3 = horzcat(ktemp{:}).' ;
K3 = horzcat(ptemp{:}).' ;
Ek3=E3-K3 ;
Inv_Ek= inv(Ek3) ;
F3=[1+w0;1+w1;1+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)(2*exp(x)-1) ;
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=8','aproksimasi N=2'},'Location','Northwest')
%plot(xx,y3)
%title('Error N=2')
%grid on
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