Parameter Estimation - Environmental Modeling - page 207

1

given
modelled

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x

Fig. 10.8 Optimal fit for diffusivity estimation example problem

function par_est2a
….
function f = myfun(D);
global xfit cfit Q
options = bvpset;

% solve diffusion equation for c with c(0)=1 and dc/dx(1)=0
solinit = bvpinit([0 xfit 1],@guess);
c = bvp4c (@mat4ode,@mat4bc,solinit,options,Q/D,1);

% solve Poisson equation for dc/dD (cD) with boundary conditions
solinit = bvpinit([0 xfit 1],@guess1);
cD = bvp4c (@mat4ode,@mat4bc,solinit,options,Q/D/D,0);

% specify function f to vanish
f = 2*(c.y(1,2:size(c.y,2)-1)-cfit)*cD.y(1,2:size(c.y,2)-1)';

function dydx = mat4ode(x,y,Q,c0)
dydx = [y(2); -Q];

% ------------------------------------------------------------
function res = mat4bc(y0,y1,Q,c0)
res = [y0(1)-c0; y1(2)];

% ------------------------------------------------------------
function v = guess(x)
v = [x*(x-2)+1; 2*(x-1)];

% ------------------------------------------------------------
function v = guess1(x)
v = [x*(x-2); 2*(x-1)];