Code covered by the BSD License  

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Euler’s method

Euler’s method

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find the function then draw it using the derivative Euler’s method

Euler
function Euler
fprintf('This program help you to find Euler method iteration \n');
fprintf('Created By Mohammed Kayed');
pause
clc
clear
syms x y;
f(x,y)=input('Y''=');
func=char(f(x,y));
X0=input('X0=');
Y0=input('Y0=');
h=input('step size =');
fprintf('\nIf you want to choose the number of iteration press 1 \n');
fprintf('If you want to find the solution at some point press 2 \n');
n=input('Your chioce --> ');
if n==1
    n=input('the # of iteration =');
    clc
    fprintf('Y''=%s \t Step size = %g \t # of iteration = %g\n',func,h,n);
    disp('---------------------------------------------')
    fprintf('\n\n# of iteration \t\t Xn \t\t\t Yn\n');
     Q=zeros(1,n+1);
       W=zeros(1,n+1);
    for i=0:n
       Q(1,i+1)=X0;
       W(1,i+1)=Y0;
    fprintf('\t\t %5g \t\t\t %+f \t\t %+f \n',i,X0,Y0);
     Y0=double(Y0+h*f(X0,Y0));
     X0=X0+h;
    end
    plot(Q,W);
else
n=input('The value of X you want to stop at =');
 Q=zeros(1,n+1);
       W=zeros(1,n+1);
clc
fprintf('Y''=%s \t Step size = %g \t # of iteration = %g\n',func,h,(n-X0)/h+1);
    disp('---------------------------------------------')
    fprintf('\n\n# of iteration \t\t\t  Xn \t\t\t\t   Yn\n');
    i=0;
    while 1
        Q(1,i+1)=X0;
       W(1,i+1)=Y0;
        fprintf('\t\t%2g  \t\t\t %+f  \t\t %+f \n',i,X0,Y0);
        if X0>=n
        break
        end
     Y0=double(Y0+h*f(X0,Y0));
     X0=X0+h;
     i=i+1;
    end
     plot(Q,W);
end

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