clear();
a = 0;
b = 2;
T = 1;
Nx = 200;
Nt = 400;
sigma = 0.5;

function y = u_exact(x,t)
    y = t*t*exp(x);
endfunction

function y=f(x,t)
    y= (2*t-t*t)*exp(x);
endfunction

function y=err(Nx,Nt,u_ex)
    y = abs( solve(Nx,Nt) - u_ex );
endfunction

function y=progonka(A,B,C,D)
    // A,B,C,D - массивы поддиагональных эл-в, диагональных, наддиагональных и правой части соответственно
    N = length(B);
    c(1) = C(1)/B(1);
    d(1) = D(1)/B(1);
    for i = 2:N-1
        k = B(i) - A(i)*c(i-1);
        c(i) = C(i)/k;
        d(i) = (D(i) - A(i)*d(i-1))/k;
    end
    y(N) = (D(N) - A(N)*d(N-1))/(B(N) - A(N)*c(N-1));
    for i = N-1:-1:1
        y(i) = d(i) - c(i)*y(i+1);
    end
endfunction

//u_0 = 0 в нашем случае
function y=solve(Nx,Nt)
    h = (b-a)/Nx;
    tau = T/Nt;
    x = a:h:b;
    t = 0:tau:T;

    U = zeros(Nt+1,Nx+1);
    A = zeros(Nx+1,1);
    B = zeros(Nx+1,1);
    C = zeros(Nx+1,1);
    D = zeros(Nx+1,1);

    //цикл по t
    for n = 1:Nt


    //Заполняем диагонали
    for i = 2:Nx
        B(i) = -h*h-2*tau*sigma;
        A(i) = tau*sigma;
        C(i) = tau*sigma;
        D(i) = (-h*h+2*tau*(1-sigma))*U(n,i)-tau*(1-sigma)*(U(n,i+1)+U(n,i-1))-tau*h*h*f(x(i),t(n));
    end

// Граничные условия
C(1) = 4 + B(2)/C(2);
B(1) = -3 + A(2)/C(2);
D(1) = 2*t(n+1)*t(n+1)*h + D(2)/C(2);

B(Nx+1) = 3  - C(Nx)/A(Nx);
A(Nx+1) = -4 - B(Nx)/A(Nx);
D(Nx+1) = 2*t(n+1)*t(n+1)*h*exp(b) - D(Nx)/A(Nx);

U(n+1,:) = progonka(A,B,C,D)';

end
y = U;
endfunction


U = solve(Nx,Nt);

    h = (b-a)/Nx;
    tau = T/Nt;
    x = a:h:b;
    t = 0:tau:T;




for i=1:Nx+1
    for n=1:Nt+1
        U_ex(n,i) = u_exact(x(i),t(n));
        end
end


f1=scf(1);  //creates figure with id==4 and make it the current one
f1.color_map = jetcolormap(64);
xtitle ('x', 't', 'exact_solution');
plot3d1(t,x,U_ex);

f2=scf(2);  //creates figure with id==4 and make it the current one
f2.color_map = jetcolormap(64);
xtitle ('x', 't', 'U');
plot3d1(t,x,U);

f3=scf(3);  //creates figure with id==4 and make it the current one
f3.color_map = jetcolormap(64);
xtitle ('x', 't', 'error');
mis=max(err(Nx,Nt,U_ex));
plot3d1(t,x,err(Nx,Nt,U_ex));
/*
// pogresnosti
NxL = [50, 100,200,400,800];
NtL = [25,100,400,1600,6400];
errL = zeros(5);

for j = 1:5
    Nx = NxL(j);
    Nt = NtL(j);

    h = (b-a)/Nx;
    tau = T/Nt;
    x = a:h:b;
    t = 0:tau:T;

    U_ex = zeros(Nt+1,Nx+1);


for i=1:Nx+1
    for n=1:Nt+1
        U_ex(n,i) = u_exact(x(i),t(n));
        end
end
    errL(j) = max(err(Nx,Nt,U_ex));
end

*/