can anyone help me graph numerical solutions and exact solutions
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clear;
clc;
format long g
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-EA)*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; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1];
C=inv(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)(cos(x))
uaa=[];
xx=[];
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'
Err=abs(uaa'-uee')
y=(abs(uaa-uee));
[xx uee uaa y];
uee;
uaa;
y;
plot(xx,uaa,'o',xx,uee,'r')
grid on
plot(xx,y)
grid on
toc
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