#####    cont1.mod     ####    modelfile for problem 1   ####
#
param n default 39;
param n1 := n+1;
param a default .01;
param g default 20;

var x{0..n1, 0..n1};

param h := 1/n1;
param h2 := h^2;

param yd{i in 1..n, j in 1..n} := 3 + 5*i*(i*h-1)*j*(j*h-1)*h2;

minimize f:	h2*sum{i in 1..n, j in 1..n} 
(x[i,j]-yd[i,j])^2 + h*a*sum{i in 1..n, j in {0,n1}} (x[i,j]^2+x[j,i]^2);

s.t. pde{i in 1..n, j in 1..n}:
	4*x[i,j] - sum{k in {-1,1}} (x[i+k,j] + x[i,j+k]) = g*h2;

s.t. sc{i in 1..n, j in 1..n}:  0 <= x[i,j] <= 3.5;

s.t. cc1{i in 1..n, j in {0,n1}}: 0 <= x[i,j] <= 10;    # control constraints
s.t. cc2{i in 1..n, j in {0,n1}}: 0 <= x[j,i] <= 10;    # control constraints