Abdul Azis Rahmansyah P2700213006

Kelas B

TUGAS 2

PERBANDINGAN METODE SCANNING, METODE NEWTON RAPHSON, DAN

METODE SECANT.

Mencari akar-akar Persamaan f(x) = Bx3 + Cx2 + Dx + E menggunakan matlab.

NIM : P2700213006

Maka B = 2

C = 1

D = 3

E = 6

Sehingga persamaan menjadi f(x) = 2x3 + 1x2 + 3x + 6

Program ini di buat dalam model GUI dengan inputan sesuai model rumus yang telah di

tampilkan. GUI ini telah mencakup metode scanning, Newton raphson, dan secant sehingga

dapat langsung di bandingkan hasil Perolehan nilai. Khusus untuk metode Newton raphson

turunan harus di input terlebih dahulu di fungsi g(x) dengan fungsi bantu cek turunan. Untuk

plot metode scanning membandingkan plot f(x) dengan x, tetapi untuk metode Newton raphson

dan metode secant plot yang di tampilkan membandingkan antara f(x) dengan nilai “x

perkiraan”

Tampilan awal GUI sebagai berikut :

Abdul Azis Rahmansyah P2700213006

Kelas B

Setelah di jalankan dengan inputan yang telah di tentukan dapat di lihat seperti gambar berikut

:

Di mana program membaca nilai akar adalah -1.2405 untuk persamaan

f(x) = 2x3 + 1x2 + 3x + 6

untuk metode scanning toleransi di atur sedemikian rupa agar di peroleh titik yang dapat

menampilkan nilai f(x) = 0.

Abdul Azis Rahmansyah P2700213006

Kelas B

plot untuk metode scanning seperti berikut :

Di mana titik f(x) = 0 di tandai dengan titik o pada plot sebagai tanda bahwa terdapat nilai x

yang melewati titik sehingga f(x) = 0

Sedang untuk metode Newton raphson hasil perbandingan nilai perhitungan yang tampil di

command matlab sebagai berikut :

Abdul Azis Rahmansyah P2700213006

Kelas B

Untuk metode Secant hasil perbandingan nilai perhitungan sebagai berikut :

Untuk listing program sebagai berikut :

Listing GUI metode scanning dan listing plot scanning function run_Callback(hObject, eventdata, handles) % hObject handle to run (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) As = get(handles.A,'string'); Bs = get(handles.B,'string'); Cs = get(handles.C,'string'); Ds = get(handles.D,'string'); Es = get(handles.E,'string'); mins = get(handles.minimum,'string'); maxs = get(handles.maximum,'string'); intervals = get(handles.interval,'string'); stoleransi = get(handles.stoleransi,'string'); A=str2num(As); B=str2num(Bs); C=str2num(Cs); D=str2num(Ds); E=str2num(Es); minxx=str2num(mins); maxxx=str2num(maxs); intervalxx=str2num(intervals); Tol=str2num(stoleransi); akar=[]; a=1; d=1; x=minxx:intervalxx:maxxx; akhir=maxxx-minxx+1; z=length(x); akar=[]; for j=1 :z y(j) = (A*x(j)^4) +(B*x(j)^3) + (C*x(j)^2) + (D*x(j)) + E; % pengujian pencarian titik 0 if y(j)>=(-Tol) && y(j)<=(Tol)

Abdul Azis Rahmansyah P2700213006

Kelas B

akar(d)=x(j); d=d+1; end % save data y; end akar set(handles.hasilscan,'string',akar); ind=find(y >=(-Tol) & y <= Tol); xx=minxx:intervalxx:maxxx; axes(handles.axes1); cla; plot(xx,y,xx(ind),y(ind),'o');axis tight; % axes(handles.axes1); cla; plot(y);axis tight;text(0.2,0,'\fontsize{8}

P2700213006') handles.y=y; handles.Tol=Tol; handles.minxx=minxx; handles.maxxx=maxxx; handles.akhir=akhir; handles.intervalxx=intervalxx; guidata(hObject,handles);

% --- Executes on button press in grafik. function grafik_Callback(hObject, eventdata, handles) % hObject handle to grafik (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) handles = guidata(gcbo); y=handles.y; Tol=handles.Tol; minxx=handles.minxx; maxxx=handles.maxxx; intervalxx=handles.intervalxx; akhir=handles.akhir;

ind=find(y >=(-Tol) & y <= Tol); x=minxx:intervalxx:maxxx; figure(1),plot(x,y,x(ind),y(ind),'o'),axis tight,grid

Listing cek turunan, Listing metode Newton raphson dan listing plot Newton raphson % --- Executes on button press in nrcek. function nrcek_Callback(hObject, eventdata, handles) % hObject handle to nrcek (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) Asnr = get(handles.nrA,'string'); Bsnr = get(handles.nrB,'string'); Csnr = get(handles.nrC,'string'); Dsnr = get(handles.nrD,'string'); Esnr = get(handles.nrE,'string'); Anr=str2num(Asnr); Bnr=str2num(Bsnr); Cnr=str2num(Csnr); Dnr=str2num(Dsnr); Enr=str2num(Esnr); syms x; y = (Anr*x^4) +(Bnr*x^3) + (Cnr*x^2) + (Dnr*x) + Enr; z=diff(y); l=char(z); set(handles.nrhasilcek,'string',l);

Abdul Azis Rahmansyah P2700213006

Kelas B

% --- Executes on button press in nrrun. function nrrun_Callback(hObject, eventdata, handles) % hObject handle to nrrun (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) Asnr = get(handles.nrA,'string'); Bsnr = get(handles.nrB,'string'); Csnr = get(handles.nrC,'string'); Dsnr = get(handles.nrD,'string'); Esnr = get(handles.nrE,'string'); Fsnr = get(handles.nrF,'string'); Gsnr = get(handles.nrG,'string'); Hsnr = get(handles.nrH,'string'); Isnr = get(handles.nrI,'string'); awalnr = get(handles.nrawal,'string'); epsilonnr = get(handles.nrepsilon,'string'); Anr=str2num(Asnr); Bnr=str2num(Bsnr); Cnr=str2num(Csnr); Dnr=str2num(Dsnr); Enr=str2num(Esnr); Fnr=str2num(Fsnr); Gnr=str2num(Gsnr); Hnr=str2num(Hsnr); Inr=str2num(Isnr); X=str2num(awalnr); Ep=str2num(epsilonnr); i=0; M=9; xb=0; disp('_________Metode Newton Raphson_________________'); disp('_______________________________________________'); disp(' i xi f(xi) epsilon'); disp('_______________________________________________'); a=1; b=1; while (Ep<M) fx= (Anr*X^4) +(Bnr*X^3) + (Cnr*X^2) + (Dnr*X) + Enr; gx= (Fnr*X^3) + (Gnr*X^2) + (Hnr*X) + Inr; fxx(a)=fx; xb=X-(fx/gx); M= abs(X-xb); X=xb; xc(b)=xb; i=i+1; a=a+1; b=b+1; fprintf('%3.0f %12.6f %12.6f %12.6f\n',i,xb,fx,M); end disp('------------------------------') fprintf('Akarnya Adalah = %10.8f\n',xb); set(handles.nrakar,'string',xb); fx= (Anr*X^4) +(Bnr*X^3) + (Cnr*X^2) + (Dnr*X) + Enr; gx= (Fnr*X^3) + (Gnr*X^2) + (Hnr*X) + Inr; fxx(a)=fx; xb=X-(fx/gx); M= abs(X-xb); X=xb;

Abdul Azis Rahmansyah P2700213006

Kelas B

xc(b)=xb; i=i+1; a=a+1; b=b+1; axes(handles.nrhasilplot); cla; plot(xc,fxx);axis tight; handles.xc=xc; handles.fxx=fxx; guidata(hObject,handles);

% --- Executes on button press in nrplot. function nrplot_Callback(hObject, eventdata, handles) % hObject handle to nrplot (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) handles = guidata(gcbo); xc=handles.xc; fxx=handles.fxx; figure(2),plot(xc,fxx),grid on

Listing metode secant dan listing plot secant % --- Executes on button press in runse. function runse_Callback(hObject, eventdata, handles) % hObject handle to runse (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) Ase = get(handles.Ase,'string'); Bse = get(handles.Bse,'string'); Cse = get(handles.Cse,'string'); Dse = get(handles.Dse,'string'); Ese = get(handles.Ese,'string'); x1se = get(handles.x1se,'string'); x2se = get(handles.x2se,'string'); tolse = get(handles.tolse,'string'); Ae=str2num(Ase); Be=str2num(Bse); Ce=str2num(Cse); De=str2num(Dse); Ee=str2num(Ese); x1e=str2num(x1se); x2e=str2num(x2se); tole=str2num(tolse); disp('Program Metode Secant'); disp('=============================');

i=0; M=9; disp('_______________________________________________'); disp(' i xi f(xi) epsilon'); disp('_______________________________________________'); a=1; b=1; while (tole<M) fx= Ae*(x1e)^4 + Be*(x1e)^3 + Ce*(x1e)^2 + De*(x1e) + Ee; fxb= Ae*(x2e)^4 + Be*(x2e)^3 + Ce*(x2e)^2 + De*(x2e) + Ee; fxse(a)=fx;

Abdul Azis Rahmansyah P2700213006

Kelas B

d = x2e - (fxb*(x2e-x1e)/(fxb-fx)); M=abs(x1e-x2e); x1e = x2e; x2e = d; x22(b)=x2e; i=i+1; a=a+1; b=b+1; fprintf('%3.0f %12.6f %12.6f %12.6f\n',i,x2e,fx,M); end; disp('_______________________________________________'); fprintf('Akarnya Adalah = %10.8f\n',x2e); set(handles.akarse,'string',x2e); axes(handles.sehasilplot); cla; plot(x22,fxse);axis tight; handles.x22=x22; handles.fxse=fxse; guidata(hObject,handles);

% --- Executes on button press in plotse. function plotse_Callback(hObject, eventdata, handles) % hObject handle to plotse (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) handles = guidata(gcbo); x22=handles.x22; fxse=handles.fxse; figure(3),plot(x22,fxse),grid on