AdvDiffJump.m

%% Advection-diffusion equation with a jump
% Nick Trefethen, November 2010

%%
% (Chebfun example ode-linear/AdvDiffJump.m)
% [Tags: #linearODE, #piecewise, #advectiondiffusion]

%%
% The solution to the advection-diffusion problem
% 
% $$ 0.2u'' + u' = -1, ~~    u(-10) = u(10) = 1 $$
%
% has a boundary layer at the left:

LW = 'linewidth'; lw = 2; FS = 'fontsize'; fs = 8;
N = chebop(-10,10);
N.op = @(u) 0.2*diff(u,2) + diff(u);
N.bc = 'dirichlet';
u = N\-1; 
plot(u,LW,lw), grid on
axis([-10.1 10 0 20])

%%
% Suppose the advection is only turned on on the right
% half of the domain?
figure
N.op = @(x,u) 0.2*diff(u,2) + (x>=0).*diff(u);
N.bc = 'dirichlet';
v = N\-1; 
plot(v,'r',LW,lw), grid on
axis([-10.1 10 0 75])

%%
% For fun we can plot both solutions on the same axis.
plot(u,'b',v,'--r',LW,lw), grid on
axis([-10.1 10 0 75])