diferencas_finitas.m

function [w] = diferencas_finitas
    a = 1;
    b = 2;
    w_start = 0;
    w_final = log(256);
    h = 0.05;
    n = -1 + (b - a)/h;

    a_v = [1:n];
    b_v = [1:n];
    c_v = [1:n];
    d_v = [1:n];

    l = [1:n];
    u = [1:n];
    z = [1:n];
    t = [1:n];

    for i = 1:n
        w(i) = w_start + i * h * (w_final - w_start)/(b - a);
    end

    iteracoes = 0;

    while(iteracoes < 10)
        % Calculo dos valores da primeira linha da matriz
        k = a + h;
        t = (w(2) - w_start)/(2*h);
        a_v(1) = 2 + h*h*fy(k, w(1), t);
        b_v(1) = -1 + h*fy_linha(k, w(1), t)/2;
        d_v(1) = -(2*w(1) - w(2) - w_start + h*h*f(k, w(1), t));
        
        % Calculo dos valores dos valores das linhas 2 ate n-1 da matriz
        i = 2;
        while(i <= (n-1))
            k = a + i*h;
            t = (w(i+1) - w(i-1))/(2*h);
            a_v(i) = 2 + h*h*fy(k, w(i), t);
            b_v(i) = -1 + h*fy_linha(k, w(i), t)/2;
            c_v(i) = -1 - h*fy_linha(k, w(i), t)/2;
            d_v(i) = -(2*w(i) - w(i+1) - w(i-1) + h*h*f(k, w(i), t));
            i = i + 1;
        end

        % Calculo dos valores da linha n da matriz
        k = b - h;
        t = (w_final - w(n-1))/(2*h);
        a_v(n) = 2 + h*h*fy(k, w(n), t);
        c_v(n) = -1 - h*fy_linha(k, w(n), t)/2;
        d_v(n) = -(2*w(n) - w(n-1) - w_final + h*h*f(k, w(n), t));

        % Resolvendo a matriz
        l(1) = a_v(1);
        u(1) = b_v(1)/a_v(1);

        i = 2;
        while(i <= (n-1))
            l(i) = a_v(i) - c_v(i)*u(i-1);
            u(i) = b_v(i)/l(i);
            i = i + 1;
        end

        l(n) = a_v(n) - c_v(n)*u(n-1);

        z(1) = d_v(1)/l(1);

        for i = 2:n
            z(i) = d_v(i) - c_v(i)*z(i-1)/l(i);
        end


        t(n) = z(n);
        w(n) = w(n) + t(n);

        i = n-1;
        while(i >= 1)
            t(i) = z(i) - u(i)*t(i+1);
            w(i) = w(i) + t(i);
            i = i-1;
        end

        iteracoes = iteracoes + 1;
    end

end