Spline.m

function [t] = Spline(fun,aa,bb,n,z)

for i = 1:n
    x(i) = aa + i * ((bb-aa)/n));
    f(i) = fun(x(i));
end

for i = 2:n
    h(i) = x(i) - x(i-1);
end

for i = 2:n-1
    A(i) = h(i);
    B(i) = h(i+1);
    C(i) = 2 * (h(i)+ h(i+1));
    F(i) = 6 * ((f(i+1)-f(i)/h(i+1)) - ((f(i)-f(i-1))/h(i)));
    u(t) = diff(fun(t),2);
    u0 = u(aa);
    un = u(bb);
    a(1) = 0;
    b(1) = u0;

    for i = 1:n-1
        a(i+1) = (-B(i) / (A(i)*a(i) + C(i)));
        b(i+1) = ( (F(i)-A(i)*b(i)) / (A(i)*a(i)+C(i)) );
    end

    c(n) = un;
    for i = n-1:1
        c(i) = a(i+1) * c(i+1) + b(i+1);
    end

    c(0) = u0;
    for i = 2:n
        d(i) = (c(i)-c(i-1)) / h(i);
        b(i) = ((h(i) * c(i)) / 2) - (((h(i)^2) * d(i)/6) + ((f(i)-f(i-1))/h(i));
        a(i) = f(i);
    end

    for i = 2:n
        if (x(i-1)<=z) && (z<=x(i))
            t = a(i) + b(i)*(z-x(i)) + (c(i)/2)*(z-x(i))^2 + (d(i)/6)*(z-x(i))^3
            break
        end
    end


end