#####    cont7.mod     ####    modelfile for problem 7   ####
#
param n default 49;
param n1 := n+1;
param n4 := n*4;
param a default 0.01;

var x{0..n1, 0..n1};
var u{1..n4};

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

param yd{i in 1..n, j in 1..n} := 2 - 2*(i*h*(i*h-1)+j*h*(j*h-1));

minimize f:	.5*h2*sum{i in 1..n, j in 1..n} (x[i,j]-yd[i,j])^2 +
		.5*h*a*sum{i in 1..n4} u[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]) - h2*(x[i,j] - x[i,j]^3) = 0;

s.t. bc1 {i in 1..n}: x[i,0] - x[i,1] = h * u[i];
s.t. bc2 {i in 1..n}: x[n1,i] - x[n,i] = h * u[n+i];
s.t. bc3 {i in 1..n}: x[i,n1] - x[i,n] = h * u[2*n+i];
s.t. bc4 {i in 1..n}: x[0,i] - x[1,i] = h * u[3*n+i];

s.t. sc{i in 0..n1, j in 0..n1}: 0 <= x[i,j] <=  2.7;

s.t. cc{i in 1..n4}: 1.8 <= u[i] <= 2.5;    # control constraints