Metode Numerik dengan Menggunakan Processing

Metode Bagi Dua

Listing Program :

import java.text.DecimalFormat;

                /*menghitung akar f(x)=3e^x-2x^2 + 5 dengan metoda bagi dua

                 */

                 static double fx(double x)

                 {

                                double f_x;

                                double e=2.718281828459;

                                f_x = (3*Math.pow(e,x))-(2*Math.pow(x,2))+5;

                                return f_x;

                 }

                 public static void main(String args[])

                 {

                                int i; //untuk menghitung banyaknya iterasi

                                DecimalFormat df1=new DecimalFormat("##0.000000");

                                double e1=0.000001; //batas selang setelah iterasi

                                double e2=0.0000001; //batas nilai f(x) mendekati nol

                                double fa,fb,fc;

                                fc=1000;//nilai fungsi f(x) pada titik a,b,c

                                double a,b,c;//variabel untuk selang a,b dan c sebagai titik tengah

                                a=-1.7;b=-1.6;c=0;//nilai selang awal a dan b

                                i=0;

                                System.out.println("----------------------------------");

                                System.out.println("i\t\ta\t\t\t\tb\t\t\tc\t\t\tf(c)");

                                System.out.println("----------------------------------");

                                while((Math.abs(a-b)>e1)||(fc>e2))

                                {

                                                c=(a+b)/2;

                                                fa=fx(a);fx(b);fc=fx(c);

                                                System.out.println(i+"  "+df1.format(a)+"\t\t"+ df1.format(b)+"\t\t" + df1.format(c)+"\t\t"+df1.format(fc));

                                                if((fa*fc)<0)

                                                {

                                                                //selang baru a-c

                                                                b=c;

                                                }

                                                else

                                                {

                                                                //selang baru b-c

                                                                a=c;

                                                }

                                                i++;

                                }

                                System.out.println("----------------------------------");

                                System.out.println("Hampiran akar = " + df1.format(c));

}

Metode Biseksi

Listing Program :

public static void main(String[]args){

 double x1=-1;

 double x2=3;

 double xt;

 double y1,y2,yt;

 int iterasi=33;

 for(int i=1;i<=iterasi;i++){

 y1=f(x1);

                y2=f(x2);

                xt=(x1+x2)/2;

 yt=f(xt);

 if(y1==0||y2==0){

 break;

 }

 if(y1*yt<0){

 x1=x1;

                                x2=xt;

 }

                                else if(y2*yt<0){

 x1=xt;

 x2=x2;

 }

                                else{

 System.out.println("Tidak terdapat akar " + "dalam interval ["+x1+", "+x2+"]");

                break;

 }

 System.out.println("Iterasi ke-"+i+"\txt = "+xt);

 }

}

 static double f(double x){

 return Math.pow(x,3)+4*Math.pow(x,2)-10;

 }

Metode Regula Falsi

Listing Program :

import java.text.DecimalFormat;

                /*menghitung akar f(x)=3e^x-2x^2 + 5 dengan metoda regula falsi pada selang a=-2 dan b=-1*/

                 public static double fx(double x)

                 {

                                double f_x;

                                double e=2.718281828459;

                                f_x = (3*Math.pow(e,x))-(2*Math.pow(x,2))+5;

                                return f_x;

                 }

                 public static void main(String args[])

                 {

                                int i; //untuk menghitung banyaknya iterasi

                                DecimalFormat df1=new DecimalFormat("##0.000000");

                                double e1=0.000001; //batas lebar selang setelah iterasi

                                double e2=0.0000001; //batas nilai f(x) mendekati nol

                                double fa,fb,fc;

                                fc=1000;//nilai fungsi f(x) pada titik a,b,c

                                double a,b,c;//variabel untuk selang a,b dan c sebagai titik tengah

                                a=-2;b=-1;c=0;//nilai selang awal a dan b

                                i=0;

                                System.out.println("---------------------------------");

                                System.out.println("i\t\ta\t\t\t\tb\t\t\tc\t\t\tf(c)");

                                System.out.println("---------------------------------");

                                while((Math.abs(a-b)>e1))

                                {

                                                fa=fx(a);fb=fx(b);

                                                c=b-(fb*(b-a)/(fb-fa));

                                                fc=fx(c);

                                                System.out.println(i+"  "+df1.format(a)+"\t\t"+ df1.format(b)+"\t\t" + df1.format(c)+"\t\t"+df1.format(fc));

                                                if(Math.abs(fc)<e2)

                                                {

                                                                //akar adalah c

                                                                a=c;b=c;

                                                }

                                                else

                                                {              if(fa*fc<0)b=c;

                                                                else

                                                                                a=c;       

                                                }

                                                i++;

                                }

                                System.out.println("---------------------------------");

                                System.out.println("Hampiran akar = " + df1.format(c));

                 }

Metode Newton-Raphson

Listing Program :

public static void main(String[]args){

 double x=3;

 double y,t;

 int iterasi=33;

 for(int i=1;i<=iterasi;i++){

 y=Math.pow(x,3)+4*Math.pow(x,2)-10;

 t=3*Math.pow(x,2)+8*x;

 x=x-y/t;

 if(y==0) break;

 System.out.println("Iterasi ke-"+i+"\tx= "+x);

 }

}

Metode Secant

Listing Program :

public static void main(String[]args)

{

double a=0.5;

double b=1;

double fa;

double fb;

double c;

double lebar=0;

for(int i=0; i<60; i++)

{

//rumus untuk secant

fa=Math.pow(Math.E,a)-5*Math.pow(a,2);

fb=Math.pow(Math.E,b)-5*Math.pow(b,2);

c=b-(fb*(b-a)/(fb-fa));

lebar=c-a;

a=b;

b=c;

if(fa==fb)

{

break;

}

       //mencetak hasil pencarian akar

System.out.println("Iterasi ke- "+i+"\tNilai tengah : "+c +"\tlebar :"+lebar +"\tGalat:"+fb);

}

}