You need to do element-wise opeerations in your ‘u’ function, so:
u = @(x,y)(-4*pi*exp(-5*pi*pi*0.5).*cos(2*pi*x).*sin(pi*y))./(2 + exp(-5*pi*pi*0.5).*sin(2*pi*x).*sin(pi*y));
instead of:
u = @(x,y)(-4*pi*exp(-5*pi*pi*0.5)*cos(2*pi*x)*sin(pi*y))/(2 + exp(-5*pi*pi*0.5)*sin(2*pi*x)*sin(pi*y));
With that change, it works —
exact_u
function exact_u
%u = @(x,y)(-4*0.01*pi*exp(-5*pi*pi*(0.01)*0.5)*cos(2*pi*x)*sin(pi*y))/(2 + exp(-5*pi*pi*(0.01)*0.5)*sin(2*pi*x)*sin(pi*y));
u = @(x,y)(-4*pi*exp(-5*pi*pi*0.5).*cos(2*pi*x).*sin(pi*y))./(2 + exp(-5*pi*pi*0.5).*sin(2*pi*x).*sin(pi*y));
[X,Y]=meshgrid(0:0.1:1);
Z = u(X,Y);
figure
surf(X,Y,Z);
title('U(x,y)');
xlabel('x');
ylabel('y');
zlabel('u');
grid on
box on
%Interpolation
[X1,Y1] = meshgrid(0:0.05:1);
Z1 = interp2(X,Y,Z,X1,Y1);
figure
surf(X1,Y1,Z1)
title('U(x,y)');
xlabel('x');
ylabel('y');
zlabel('u');
grid on
box on
end
.
