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KUIS 1 FISKOM CUYY

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Maria Oktavia Krisanti
1116100057
 Matriks Jacobian
function J=Jacobs (func,x,delta)
N=length(x);
for i=1:N
xjalan1=x;
xjalan1(i)=x(i)+delta;
xjalan2=x;
xjalan2(i)=x(i)-delta;
J(:,i)=(feval(func,xjalan1)-feval(func,xjalan2))/(2*delta);
end
end
Penyelesaian:
>> F= @(x)[x(1)^2+x(2)^2+x(3)-14;x(1)^2+2*x(2)^2-9;x(1)3*x(2)^2+x(3)]
F =
@(x)[x(1)^2+x(2)^2+x(3)-14;x(1)^2+2*x(2)^2-9;x(1)3*x(2)^2+x(3)]
NewtRaphApproxBaru(F,[1;1;1],1e-5,10000)
ans =
1.5616
1.8113
8.2808
>> feval(F,ans)
ans =
0
0
0
 Invers Matriks Jacobian dengan Gauss-Jordan
function p=invJacobs(A)
[a b]=size(A);
c=[A eye(a,b)];
if a~=b
Error('matriks A bukan matriks persegi')
pause
else
for ii=2:a
d=c(ii:a,ii-1)/c(ii-1,ii-1);
c(ii:a,:)=c(ii:a,:)-d*c(ii-1,:);
end
for jj=a-1:-1:1
u=c(jj:-1:1,jj+1)/c(jj+1,jj+1);
c(jj:-1:1,:)=c(jj:-1:1,:)-u*c(jj+1,:);
end
for k=1:a
c(k,:)=c(k,:)/c(k,k);
end
p=c(:,a+1:2*a);
end
end
 Aproksimasi Newton-Raphson
function m=Newton_Raphson (x,niter)
%call fungsi.m
%call Central.m
%m=zeros(niter,1)
m(1)=x;
for ii=1:niter-1
m(ii+1)=m(ii)-(fungsi(m(ii))/Central(m(ii),1e-6));
fprintf('Iterasion=%iSolusi=%.4f\n',ii,m(ii+1));
if abs(m(ii+1)-m(ii))<1e-6;
disp('Solusi Konvergence')
break
end
if fungsi(m(ii+1))==0
disp ('Solusi Eksak telah ditemukan')
break
end
end
2. Menghitung ketinggian maksimum, waktu tempuh mencapai tanah,
dan jarak maksimum mencapai tanah
 Fungsi Vy(t)
function Vy=Vy (V0,theta,g,t)
Vy=V0*sind(theta)-g*t;
end
 Fungsi y(t)
function y=y2(V0,y0,theta,g,t)
y=y0+(V0*sind(theta)*t)-(0.5*g*(t^2));
end
 Fungsi y(x)
function y=y1(V0,y0,theta,g,x)
y=y0+(x*tand(theta))-((g*x^2)/2*cosd((theta)^2*V0^2));
end
 Fungsi tymax, tmax, dan xmax
function GerakParabol(V0,y0),theta,g,delta,Niter)
t(1)=0;
for i=1:Niter-1
turunan=(Vy(V0,theta,g,(t(i)+delta))-Vy(V0,theta,g,(t(i)delta)))/(2*delta);
end
thmax=t(akhir)
t1(1)=100
for i=1:Niter-1
turunan=(y2(V0,y0,theta,g,(t1(i)+delta))y2(V0,y0,theta,g,(t1(i)-delta)))/(2*delta);
t1(i+1)=t1(i)-(y2(V0,y0,theta,g,t1(i))/turunan);
end
tmax=t1(akhir)
x(1)=100;
for i=1:Niter-1
turunan=(y1(V0,y0,theta,g,(x(i)+delta))y1(V0,y0,theta,g,(x(i)-delta)))/(2*delta);
x(i+1)=x(i)-(y1(V0,y0,theta,g,x(i))/turunan);
end
xmax=x(akhir)
end
3. Finite Difference
 Fungsi awal
function F=fungsi(x)
F=exp(-3*x)+4*x^2+4;
end
 Forward:
function Forward(x,deltax) %nama fungsi
%call fungsiUWU.m
Forward =(fungsi(x+deltax)-fungsi(x))/deltax %definisi fungsi
end
 Backward:
function Backward(x,deltax) %nama fungsi
%call fungsiUWU.m
Backward =(fungsi(x)-fungsi(x-deltax))/deltax %definisi fungsi
end
 Central:
function Central(x,deltax)%nama fungsi
%call fungsiUWU.m
Central =(fungsi(x+deltax)-fungsi(x-deltax))/(2*deltax)
%definisi fungsi
end