function [x, w, yA, MutlakHata, k, J, F] = nonlineersonlufark(a,b,alpha,beta,N,TOL,M)

% y''=f(x,y,y') y(a)=alpha, y(b)=beta
% y = Y0, y'=Y1

f = @(x,Y0,Y1) ...;
fY0 = @(x,Y0,Y1) ...;                %f'in y'ye göre kısmi türevi
fY1 = @(x,Y0,Y1) ...;                % f'in y' 'ne göre kısmi türevi

h = (b-a)/N;

x = a:h:b;

w(1) = alpha; 
w(N+1) = beta; 

% ilk w değerleri

for i = 2:N
    
    w(i) = alpha + i*((beta-alpha)/(b-a))*h;
    
end


k=1;
while 1
    
    J = zeros(N-1); 
    
    % Jacobian matrisin köşegen elemanları
    
    for i = 1:N-1
        
        J(i,i) = -2 - (h^2)*fY0(x(i+1),w(i+1),(w(i+2)-w(i))/(2*h));
        
    end
    
    for i = 1:N-2
        
        J(i,i+1) = 1-(h/2)*fY1(x(i+1),w(i+1),(w(i+2)-w(i))/(2*h));
        J(i+1,i) = 1+(h/2)*fY1(x(i+2),w(i+2),(w(i+3)-w(i+1))/(2*h));
        
    end
    
    F = zeros(N-1,1);
    
    F(1,1) = 2*w(2) - w(3) + (h^2)*f(x(2),w(2),(w(3)-alpha)/(2*h))-alpha;
    
    for i = 2:N-2
        
        F(i,1)= -w(i) + 2*w(i+1) - w(i+2) + (h^2)*f(x(i+1),w(i+1),(w(i+2)-w(i))/(2*h));
        
    end
    
    F(N-1,1) = -w(N-1) + 2*w(N) + (h^2)*f(x(N),w(N),(beta-w(N-1))/(2*h))-beta;
    
    v = J\F; % v = inv(J)*F;
    
    Deltax = zeros(N+1,1);
    
    for i = 2:N
        
        Deltax(i,1) = v(i-1);
        
    end
    
    if norm(Deltax) < TOL || k>M
        break;
    end
        
    w = w + Deltax';
    
    k = k+1;
    
    
end

% Analitik çözüm

yA = ...;
    
MutlakHata = abs(yA - w);