Source Code MATLAB Metode Beda Hingga

%======================================================

%Program Berikut adalah modifikasi dari

%Program Metode Beda Hingga pada modul Persamaan Differensial Numerik

%Original Author: Prof. Dr. Agus Suryanto, M.Sc.

%======================================================

%Diketahui Masalah Kondisi Batas

%X"(t)=2*t/(1+t^2)X'(t)-2/(1+t^2)X(t)+1

%X(0)=1.25; X(1)=-0.95

%======================================================

clear all;clc;

h=input('masukkan h=');

N=(1-0)/h;

A=zeros(N+1,N+1);

X=zeros(N+1,1);

salah=0;

t=0:h:1;

A(1,1)=1;

A(N+1,N+1)=1;

for i=2:N;

    p=1+t(i)^2;

    m=h^2;

    A(i,i-1)=1+(h*t(i)/p);%a(i)

    A(i,i)=(2*m/p)-2;     %b(i)

    A(i,i+1)=1-h*t(i)/p;  %c(i)

end

F=1.25; %nilai awal

k=((1/m)+((t(i))/(h*p)));

l=((1/m)-((2*t(i))/p));

for i=1:N-1

    if i==1

        F=[F 1-k*1.25];

    elseif i==N-1

        F=[F  1+l*0.95];

    else

        F=[F  1];

    end

end

F=[F  -0.95];

B=inv(A/h^2);

X=B*transpose(F);

%penyelesaian eksak

for i=1:N+1

    y(i)=t(i)*(1/20-1/2*pi)-9/4*t(i)^2+5/4+2*t(i)*atan(t(i))+1/2*...

        log(t(i)^2+1)*t(i)^2-1/2*log(t(i)^2+1);

end

for i=1:N+1

    eror(i)=abs(y(i)-X(i));

    salah=salah+eror(i);

end

 fprintf('____________________________________________________________\n');

 fprintf('Iterasi                Nilai t(i)                Nilai X(i)\n');

 fprintf('-----------------------------------------------------------\n');

   

for i=1:N+1;

    fprintf('%f                     %f                 %f\n   ',i,t(i),X(i));

end

figure(1)

plot(t,X,'ro');

grid on;

hold on;

plot(t,y,'b*');