Tugas Metode Numerik Program Persamaan A

Tugas Metode Numerik
Program Persamaan Akar dengan Metode Newton
Rapshon

Disusun oleh :
Ifnu Dwi Jayanto
105410151

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STIMIK AKOKOM YOGYAKARTA
2016

1. Algoritma

Masukan : nilai awal (x0)
Keluaran : Akar
Langkah-langkah :
a. definisikan terlebih dahulu fungsi dan aturan fungsinya
b. jika f’(x) =0 maka proses gagal.Selesai
c. jika tidak, x r ≔ x 0

d. jika

| |
xr −x 0
xr

f ( x0 )
'
f (x 0)

≤ epsilon maka akar := xr .Selesai satu iterasi

e. ulangi iterasi dengan mengambil x0 := xr

2. Flowchart

3. Listing Program
import java.util.*;
public class Newton{
public static Scanner sc = new Scanner(System.in);

public static double[] A;
public static double[] B;
public static double relApproxErrorLimit;
public static double Finitial(double x) {
double retVal = 0.0;
for (int i = A.length - 1; i >= 0; i--)
retVal += A[i] * Math.pow(x, i);
return retVal;
}
public static double Fder(double x) {
double retVal2 = 0.0;
for (int i = B.length - 1; i >= 0; i--)
retVal2 += B[i] * Math.pow(x, i);
return retVal2;
}
public static void printTableLine() {
for(int i = 0; i < 78; i++)
System.out.print('-');
System.out.println();
}

public static void findRoot(double Sval) {
double xnew =0.0;
double xold =0.0;
double prevApprox = 0.0;
int count = 0;

printTableLine();
System.out.printf("%10s %10s %10s %10s %10s \n", "Iterasi","x", "F(x)", "F'(x)", "% Galat");
printTableLine();
while (true) {
count++;
System.out.printf("%10d %10f %10f %10f ", count, Sval, Finitial(Sval),Fder(Sval));
xnew = Sval - Finitial(Sval) / Fder(Sval);
xold = Sval;
Sval = xnew;
System.out.printf("%10f \n", Math.abs((xnew - xold) / xnew * 100.0));
if (count > 1)
if (Math.abs((xnew - xold) / xnew * 100.0) < relApproxErrorLimit)
break;

if (count % 50 == 0) {
System.out.println();
System.out.println(" #" + count + " Iterasi Telah Dilakukan.");
System.out.println(" #Ketik 't' Untuk Menghentikan Iterasi.");
System.out.println(" #Ketik Selain 't' Untuk Melanjutkan Iterasi.");
System.out.println();
System.out.print("Lanjutkan? ");
String s = sc.next();

if (s.equals("T") || s.equals("t"))
break;
System.out.println();
}
}

printTableLine();
System.out.println();
System.out.println("\t Jumlah Iterasi : " + count);
System.out.println("\tBatas % Galat Relatif : " + relApproxErrorLimit);
System.out.println("\t Hampiran Akar : " + xnew);

System.out.println();
}
public static void main(String[] args) {
int N, M,O;
double Svalue;
while (true) {
System.out.print("Nilai awal (X0): ");
Svalue = sc.nextDouble();
System.out.println();
if (Svalue>0.0)
break;
else
{
System.out.println("Nilai awal harus lebih dari 0 !");
}

}
while (true) {
System.out.print("Digit Signifikan : ");
M = sc.nextInt();

System.out.println();
if (M >= 1)
break;
else {
System.out.println(" #Jumlah Digit Signifikan Harus > 0 !");
System.out.println();
}
}
relApproxErrorLimit = 0.5 * Math.pow(10, 2 - M);
System.out.println();
findRoot(Svalue);
}
}

4. Hasil output