Studi Kasus: Metode Euler

Berikut ini adalah contoh studi kasus menggunakan Metoda Euler dengan menggunakan Matlab : 

Studi Kasus:

Interpolasi Linear

Metode Euler :

Kasus : dy/dx=4x=5

Nilai awal (x0,y0) : 0 0

Artinya x0 = 0 dan y0 = 0

Nilai akhir (x)40

Artinya akan dihitung solusi persamaan diferensial saat x=440 atau y(40)

Jumlah pita : 100

Antara x0 dan x akan dibagi 100 segmen atau pita

Hasil : 3434

Solusi persamaa diferensial y(40)=3434

Metode Euler

function varargout = metoda_euler(varargin)

% METODA_EULER MATLAB code for metoda_euler.fig

%      METODA_EULER, by itself, creates a new METODA_EULER or raises the existing

%      singleton*.

%

%      H = METODA_EULER returns the handle to a new METODA_EULER or the handle to

%      the existing singleton*.

%

%      METODA_EULER('CALLBACK',hObject,eventData,handles,...) calls the local

%      function named CALLBACK in METODA_EULER.M with the given input arguments.

%

%      METODA_EULER('Property','Value',...) creates a new METODA_EULER or raises the

%      existing singleton*.  Starting from the left, property value pairs are

%      applied to the GUI before metoda_euler_OpeningFcn gets called.  An

%      unrecognized property name or invalid value makes property application

%      stop.  All inputs are passed to metoda_euler_OpeningFcn via varargin.

%

%      *See GUI Options on GUIDE's Tools menu.  Choose "GUI allows only one

%      instance to run (singleton)".

%

% See also: GUIDE, GUIDATA, GUIHANDLES

% Edit the above text to modify the response to help metoda_euler

% Last Modified by GUIDE v2.5 18-May-2018 14:20:22

% Begin initialization code - DO NOT EDIT

gui_Singleton = 1;

gui_State = struct('gui_Name',       mfilename, ...

                   'gui_Singleton',  gui_Singleton, ...

                   'gui_OpeningFcn', @metoda_euler_OpeningFcn, ...

                   'gui_OutputFcn',  @metoda_euler_OutputFcn, ...

                   'gui_LayoutFcn',  [] , ...

                   'gui_Callback',   []);

if nargin && ischar(varargin{1})

    gui_State.gui_Callback = str2func(varargin{1});

end

if nargout

    [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});

else

    gui_mainfcn(gui_State, varargin{:});

end

% End initialization code - DO NOT EDIT

% --- Executes just before metoda_euler is made visible.

function metoda_euler_OpeningFcn(hObject, eventdata, handles, varargin)

% This function has no output args, see OutputFcn.

% hObject    handle to figure

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

% varargin   command line arguments to metoda_euler (see VARARGIN)

% Choose default command line output for metoda_euler

handles.output = hObject;

% Update handles structure

guidata(hObject, handles);

% UIWAIT makes metoda_euler wait for user response (see UIRESUME)

% uiwait(handles.figure1);

% --- Outputs from this function are returned to the command line.

function varargout = metoda_euler_OutputFcn(hObject, eventdata, handles)

% varargout  cell array for returning output args (see VARARGOUT);

% hObject    handle to figure

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

% Get default command line output from handles structure

varargout{1} = handles.output;

% --- Executes on button press in show_grap_pushbutton.

function show_grap_pushbutton_Callback(hObject, eventdata, handles)

% hObject    handle to show_grap_pushbutton (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

axes(handles.axes1);

handles.x=0:0.1:100

handles.y=4*handles.x+5;

plot(handles.x,handles.y);

title('Pers.Diff dy/dx = 4x+5');

xlabel('x');

ylabel('y');

guidata(hObject,handles);

function nilai_awal_x0_edit_Callback(hObject, eventdata, handles)

% hObject    handle to nilai_awal_x0_edit (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

% Hints: get(hObject,'String') returns contents of nilai_awal_x0_edit as text

%        str2double(get(hObject,'String')) returns contents of nilai_awal_x0_edit as a double

% --- Executes during object creation, after setting all properties.

function nilai_awal_x0_edit_CreateFcn(hObject, eventdata, handles)

% hObject    handle to nilai_awal_x0_edit (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows.

%       See ISPC and COMPUTER.

if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))

    set(hObject,'BackgroundColor','white');

end

function nilai_awal_y0_edit_Callback(hObject, eventdata, handles)

% hObject    handle to nilai_awal_y0_edit (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

% Hints: get(hObject,'String') returns contents of nilai_awal_y0_edit as text

%        str2double(get(hObject,'String')) returns contents of nilai_awal_y0_edit as a double

% --- Executes during object creation, after setting all properties.

function nilai_awal_y0_edit_CreateFcn(hObject, eventdata, handles)

% hObject    handle to nilai_awal_y0_edit (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows.

%       See ISPC and COMPUTER.

if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))

    set(hObject,'BackgroundColor','white');

end

function nilai_akhir_edit_Callback(hObject, eventdata, handles)

% hObject    handle to nilai_akhir_edit (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

% Hints: get(hObject,'String') returns contents of nilai_akhir_edit as text

%        str2double(get(hObject,'String')) returns contents of nilai_akhir_edit as a double

% --- Executes during object creation, after setting all properties.

function nilai_akhir_edit_CreateFcn(hObject, eventdata, handles)

% hObject    handle to nilai_akhir_edit (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows.

%       See ISPC and COMPUTER.

if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))

    set(hObject,'BackgroundColor','white');

end

function jml_pita_edit_Callback(hObject, eventdata, handles)

% hObject    handle to jml_pita_edit (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

% Hints: get(hObject,'String') returns contents of jml_pita_edit as text

%        str2double(get(hObject,'String')) returns contents of jml_pita_edit as a double

% --- Executes during object creation, after setting all properties.

function jml_pita_edit_CreateFcn(hObject, eventdata, handles)

% hObject    handle to jml_pita_edit (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows.

%       See ISPC and COMPUTER.

if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))

    set(hObject,'BackgroundColor','white');

end

function hasil_euler_edit_Callback(hObject, eventdata, handles)

% hObject    handle to hasil_euler_edit (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

% Hints: get(hObject,'String') returns contents of hasil_euler_edit as text

%        str2double(get(hObject,'String')) returns contents of hasil_euler_edit as a double

% --- Executes during object creation, after setting all properties.

function hasil_euler_edit_CreateFcn(hObject, eventdata, handles)

% hObject    handle to hasil_euler_edit (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows.

%       See ISPC and COMPUTER.

if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))

    set(hObject,'BackgroundColor','white');

end

% --- Executes on button press in calculate_euler_pushbutton.

function calculate_euler_pushbutton_Callback(hObject, eventdata, handles)

% hObject    handle to calculate_euler_pushbutton (see GCBO)

% eventdata  reserved - to be defined in a future version of MATLAB

% handles    structure with handles and user data (see GUIDATA)

x1 = str2num(get(handles.nilai_awal_x0_edit,'String'));

y1 = str2num(get(handles.nilai_awal_y0_edit,'String'));

x2 = str2num(get(handles.nilai_akhir_edit,'String'));

pita = str2num(get(handles.jml_pita_edit,'String'));

n=0;

delt=100;

eps=1e-3;

while (abs(delt)>eps)      %iterasi selama delt lebih besar dari eps    

n=n+1;

%pita=pow(2,n);   %2^n     

delx=(x2-x1)/pita;    

x=x1;

y=y1;    

while (x<x2)            %Pers.Differensial yang dicari solusinya          %*************************        

%fx=y;        

fx=4*x+5;        

%fx=4;       

%*************************        

y=y+fx*delx;   %iterasi Euler orde-1        

x=x+delx;    

end    

if (n>1)        

delt=y-y2;    

end    

y2=y;

end

set(handles.hasil_euler_edit,'String',num2str(y));

Lebih lengkap kamu bisa download file metode