ANALISIS NUMERIK (MENGGUNAKAN MATLAB)

ITERASI TITIK TETAP (DENGAN MENGGUNAKAN MATLAB)

%NUGRAHENI NOVITASARI (110312419011)

clc;clear;

fprintf('======================================================');

fprintf('\n n        xn:I1       xn:I2      xn=I3       xn:I4\n');

fprintf('======================================================');

x0=2.5;

x1=2.5;

x2=2.5;

x3=2.5;

fprintf('\n %g         %3.1f         %3.1f       %3.1f         %3.1f \n',0,x0,x1,x2,x3);

x4=5+x0-x0^2;x0=x4;

x5=5/x1;x1=x5;

x6=1+x2-(1/5)*x2^2;x2=x6;

x7=(1/2)*(x3+(5/x3));x3=x7;

fprintf('\n %g         %4.2f        %3.1f       %4.2f        %4.2f\n',1,x4,x5,x6,x7);

for i=2:3   

x4=5+x0-x0^2;

x5=5/x1;

x6=1+x2-(1/5)*x2^2;

x7=(1/2)*(x3+(5/x3));

x0=x4;

x1=x5;

x2=x6;

x3=x7;

fprintf('\n %g       %8.4f      %3.1f       %6.4f      %6.4f\n',i,x4,x5,x6,x7);

end;

ITERASI (DENGAN MENGGUNAKAN MATLAB)

function xn=it(xn);

xn=1+xn-(xn^2)/5;

%NUGRAHENI NOVITASARI (110312419011)

clc;clear;

x0=2.5;n=0;

fprintf('================================================\n');

fprintf(' \nn     xn              a-xn           rn        \n');

fprintf('================================================\n');

a=(5)^(1/2);

fprintf('\n%g   %5.1f            %10.2E      \n',n,x0,a-x0);

for n=1

    xn=it(x0);

    rn=(a-xn)/(a-x0);

    fprintf('\n%g     %4.2f           %10.2E    %8.4f \n',n,xn,a-xn,rn);

    x0=xn;

end;  

for n=2

    xn=it(x0);

    rn=(a-xn)/(a-x0);

    fprintf('\n%g     %6.4f         %10.2E    %8.4f \n',n,xn,a-xn,rn);

    x0=xn;

end;  

for n=3:7

    xn=it(x0);

    rn=(a-xn)/(a-x0);

    fprintf('\n%g     %6.8f     %10.2E    %8.4f \n',n,xn,a-xn,rn);

    x0=xn;

    end;   


 



CARA MEMBUAT GRAFIK ITERASI TITIK TETAP
(DENGAN MENGGUNAKAN MATLAB)

%NUGRAHENI NOVITASARI (110312419011)

clc;clear;

y=-0.3:0.0001:2;

x=0*y;%sumbu y

x0=-0.3:0.001:2;

y0=0*x0;%sumbu x

x1=0.2:0.001:1.8;

y1=x1.^3+sin(4*(x1-2))-x1.^2+0.5;%grafik

x2=y;%garis y=x

x3=1.7;

x4=0.55;

y3=0:0.05:x3;%a pada sumbu x

x5=1.55;

y4=0:0.05:x3;%b pada sumbu x

y5=1.7;

y6=0.55;

x6=0:0.05:y5;%a pada sumbu y

y7=1.55;

x7=0:0.05:y5;%b pada sumbu y

x8=1.08;

x9=1.1;

y8=0:0.05:x9;%garis pada alfa 

plot(x,y,'r',x0,y0,'r',x1,y1,x2,y,x4,y3,'.',x5,y4,'.',x6,y6,'.',x7,y7,'.',x8,y8,'.');

axis([-0.3 2 -0.3 2]);