This works:
function Script
n=0.6;
infinity=20;
solinit = bvpinit(linspace(0,infinity,30),[0 0 0 0 -1]);
sol = bvp4c(@(x,y)VK(x,y,n),@VKbc,solinit);
x = [0:2:20];
y = deval(sol,x);
for i=1:9
n = n+0.1;
sol = bvp4c(@(x,y)VK(x,y,n),@VKbc,sol);
xc{i} = sol.x;
yc{i} = sol.y;
cv{i} = (sol.y(4,:).^2+sol.y(5,:).^2).^((1-n)./(n+1)); % Calculate ‘c’
figure(i)
plot(xc{i},yc{i}, xc{i},cv{i});
title('Plots of U versus x')
ylabel('U(x)')
xlabel('x')
legend('y_1(x)', 'y_2(x)', 'y_3(x)', 'y_4(x)', 'y_5(x)', 'c(x)', 'Location','NE')
end
function yprime = VK(x,y,n)
a = ((1-n)/(n+1))*x;
c = (y(4)^2+y(5)^2)^((1-n)/(n+1));
yprime = [ c*y(4)
c*y(5)
-2*y(1) - a*c*y(4)
y(1)^2 - (y(2)+1)^2 + (y(3)+a*y(1))*c*y(4)
2*y(1)*(y(2)+1) + (y(3)+a*y(1))*c*y(5)];
end
function res = VKbc(ya,yb)
res = [ya(1);ya(2);ya(3);yb(1);yb(2)+1];
end
end
I calculated ‘c’, and created cell arrays to save the solutions at each value of ‘i’. You can use ‘xc’, ‘yc’, and ‘cv’ in other parts of your code. See the documentation on cell arrays for details on how to work with them. (In this instance, they should be relatively easy to work with. The plot call in the loop is an example of how to address them.)
I don’t know how you want your solutions to be plotted. Here, I plotted 9 separate figures, since it would be extremely difficult for you to see the individual plots if you plotted them all in one figure. I also added a legend call to each figure so you could see what the lines are.
