How to smooth out a surf plot

I want a nice and smooth surface. Can someone please give me some hints ?

clear
zspan = linspace(0,2,100);
v2in_vals = linspace(0.01,0.05,10);
v0mat = [1 0.1 1];
N = size(v0mat, 1);
zsol = cell(N,1);
v1sol = cell(N,1);
v2sol = cell(N,1);
v3sol = cell(N,1);
v2in = cell(N,1);

for k=1:length(v2in_vals)
  v0 = v0mat;
  v0(2) = v2in_vals(k);
  [z,v] = ode45(@rhs,zspan,v0);
  zsol{k} = z;
  v1sol{k} = v(:,1);
  v2sol{k} = v(:,2);
  v3sol{k} = v(:,3);
  v2in{k} = v0mat(2) * ones(size(v2sol{k}));
end

all_z = [zsol{:}];
all_v2 = [v2sol{:}];
all_v2in = [v2in{:}];

v2in_vec = v2in_vals;
z_vec = all_v2(:,2);
surf(z_vec, v2in_vec, all_v2.')
xlabel('z');
ylabel('dw');
zlabel('w');

function parameters=rhs(z,v)
            alpha=0.116; 
            db= 2*alpha-(v(1).*v(3))./(2*v(2).^2);
            dw= (v(3)./v(2))-(2*alpha*v(2)./v(1));
            dgmark= -0.01-(2*alpha*v(3)./v(1)); 
   parameters=[db;dw;dgmark];
  end

Answer 1

[KSSV]

surf(z_vec, v2in_vec, all_v2.')

Increase the dimensions of z_vec and v2in_vec. Make the difference/ step size small to increase the dimensions.