f1*f3abs(abr)

b=p

temp=crcr=cbcb=tempk=1:n

temp=arkark=abkabk=temp

xh

toc

END

BCAconst=air/arr

CB

ASTARTIII.2 Eliminasi Gauss Jordan

nj= 1:n

a=matriks koefisienc=jawaban

cr= cr*constrarj=arj*constr

tic

h=1:nr=1:n

rn

z=1:nYb=r

hr

Yp=r+1:n

abs(apr)>abs(abr)

ahz=ahz-arz*consth

b=p

ch=ch-cr*consthk=1:n

x=c

q=1:nxqXtocENDtemp=arkark=abkabk=temp

temp=crcr=cbcb=temp

consth=ahr

constr=arr

B

BA

ASTARTIII.3 LU Decompotition

j=1n

a=matriks koefisienc=jawaban

i= 1:ni=1; uii=1Uij=aij/Lii

Lij=aijtic

k=1; r=1; z=1;p=r+1; t=r

j=2:ni nz0

abs(apk)>abs(atk)YY

i=2; j=2; jumL=0;jumU=0t=tt=p

p=p+1z=1p==n

p=1:i-1x=i:n

z=0

jumL=jumL+Lxp*Upim=r; q=1

Ujy=(ajy-jumU)/LjjjumU=0q0

Lxi=axi-jumLjumL=0

temp=armarm=atmatm=temp

y=j+i:n

m=m+1q=1q=1:j-1jumU=jumU+Ljq*Uqym==n

Y

temp=crcr=ctct=tempq=0

CBA

ENDjumX=jumX+Uiz*xzz=i+1:nxi=cki-jumXCxn=cknLUckxiiXtoci=1:nYi==njumX=0i=n:-1:1cki=(ci-jumC)/LiijumC=jumC+Lir*ckrr=1:i-1jumC=0i=2:nck1=c1/L1Ujj=1; i=i+1; j=j+1B

BAanew=zerosnncnew=zerosna=matriks koefisienc=jawabanSTARTIV.1 Jacobi

i=1:nxnewi=(ci-jum)/aiii=1:niter; ej=1:njum=0xiiXei=abs((xnewi-xi)/xi)xi=xnewijijum=jum+aij*xjtocENDi=1:nmax(e)toliter=iter+1a=anew; c=cnew;e=1; iter=0cnewL=ciBAj= 1:nanewLj=aijabs(aip)>abs(aiL)n; tolp=p+1z=1z=0p==nL=pz0Yp=2; L=1; z=1i=1:nxiiXtici=1:n

BAanew=zerosnncnew=zerosna=matriks koefisienc=jawabanSTARTIV.2 Gauss Siedel

k=1:niter; ej=1:njum=0xkiXjijum=jum+aij*xjtocENDi=1:nmax(e)toliter=iter+1a=anew; c=cnew;e=1; iter=0cnewL=ciBAj= 1:nanewLj=aijabs(aip)>abs(aiL)n; tolp=p+1z=1z=0p==nL=pz0Yp=2; L=1; z=1i=1:nxiiXtici=1:n

xnewi=(ci-jum)/aiiei=abs((xnewi-xi)/xi)xi=xnewi

V.1 Newton Gregory Forward

ENDjawab(y/t)bhasilBABAj=1:n-1xcaridel=delh=x2-x1jawab=yjawab=yb=(xcari-x1)/hi=1hasil=f1delij=deli+1 j-1-deli j-1i=1:n-jj=2:n-1ndelii=fi+1-fii=1:n-1a=matriks variabelc=matriks fungsiSTART

i=i*(b-j+1)hasil=hasil+del1j*i/factorialj

V.2 Newton Gregory Backward

ENDjawab(y/t)bhasilBABAj=1:n-1xcaridel=delh=x2-x1jawab=yjawab=yb=(xcari-xn)/hi=1hasil=fndelij=deli+1 j-1-deli j-1i=1:n-jj=2:n-1ndelii=fi+1-fii=1:n-1a=matriks variabelc=matriks fungsiSTART

i=i*(b+j-1)hasil=hasil+deln-j j*i/factorialj

hasil; emax; eminENDhasil=(h/2)*jumemax=(x1-xn)*h2*yn/12emax=(x1-xn)*h2*y1/12jum=jum+yi+yi+1i=1:n-1jum=0xi=xi-1+hi=1:nyi=f(xi)i=2:n-1xi=xi-1+hn; x1; xnh=(xn-x1)/(n-1)VI.1 STARTTrapezoidal

STARTVI.2 Simpson 1/3 Rule

nnmod(n,2)==0hasil; emax; eminENDi=1:2:n-2jum=0xi=xi-1+hi=1:nyi=f(xi)i=2:n-1x1; xnh=(xn-x1)/(n-1)jum=jum+yi+4yi+1+yi+2hasil=(h/3)*jumemax=(x1-xn)*h4*yivn/180emax=(x1-xn)*h4*yiv1/180

STARTVI.3 Simpson 3/8 Rule

nnmod(n-1,3)0hasil; emax; eminENDi=1:3:n-3jum=0xi=xi-1+hi=1:nyi=f(xi)i=2:n-1x1; xnh=(xn-x1)/(n-1)jum=jum+yi+3yi+1+3yi+2+yi+3hasil=(3h/8)*jumemax=(x1-xn)*h4*yivn/80emax=(x1-xn)*h4*yiv1/80

STARTVII.1 Taylor

x1 < xcari

x1; y1; xcari; h; n

ENDy1x1=x1+hy1=jumjum=jum+(dyi*h^i)/factorialii=1:n-1jum=y1dyi= dyi-1i=3:n-1dy1=f(x1,y1)dy2=f(x1,y1)

xi=xi-1+hi=1:n-1i=2:nxi=xi-1+hn=((xcari-x1)/h)+1VII.2 STARTEuler

x1; y1; xcari; h

ENDyi+1dyi=f(xi)yi+1=yi+(h*dyi)

STARTxi=xi-1+hi=1:n-1i=2:nxi=xi-1+hn=((xcari-x1)/h)+1VII.3 Runge-Kutta

x1; y1; xcari; h

k1i=h*f(xi;yi)k2i=h*f((xi+0.5h);(yi+0.5k1i))k3i=h*f((xi+0.5h);(yi+0.5k2i))k4i=h*f((xi+h);(yi+k3i))yi+1=yi+1/6(k1i+2 k2i+2 k3i+ k4i)yi+1END

ENDxspan=[x0:increment:xf]y0[x,y]=ode45(st,xspan,y0)[x,y]plot[x,y,color/type]xlabel(x)ylabel(y)legend(ODE45)Title(..)STARTENDfunction=st(x,y)dy=persamaan turunannyaSTARTVIII.1 ODE 45

ENDxspan=[x0:increment:xf]y0[x,y]=ode23(st,xspan,y0)[x,y]plot[x,y,color/type]xlabel(x)ylabel(y)legend(ODE23)Title(..)STARTENDfunction=st(x,y)dy=persamaan turunannyaSTARTVIII.2 ODE 23