function u = economics_pde_burgers(y,t,nu_0)

% copy of Amit's burgersa.f code to numerically evaluate the Burgers
% equation for the dimension-reduced variable.

% Initialise parameters and number of points to integrate over numerically
T = 10; L = 1000;
dt = 0.01; dx = 1.0; dy = 1.0;
u = exp(-(1:L));%rand(1,10000);
Lx = L/dx;
Ly = L/dy;
nt = T/dt;

% loop multiple times to improve accuracy
for j = 1:nt

% initialise derivatives
for i = 2:Lx-1
    delu(i) = (u(i+1)-u(i-1))./(2*dy);
    delsqu(i) = (u(i+1)+u(i-1)-2*u(i))/(dy*dy);
end

% initialise periodic boundary conditions
delu(1) = (u(2)-u(Ly))/2*dy;
delu(Lx) = (u(1)-u(Ly-1))/2*dy;

delsqu(1) = (u(2)+u(Ly)-2*u(1))/(dy*dy);
delsqu(Lx) = (u(1)+u(Ly-1)-2*u(Lx))/(dy*dy);

% fixed end points
u(1) = 0;
u(Lx) = 0;

% solve equation now
for i = 1:Ly
    u(i) = u(i)+dt*(delsqu(i) - (1/sqrt(nu_0))*u(i)*delu(i));
end

end

end