Plotting graphs from equation of bvp
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Hi, I have some problems regarding bvp. It's all about plotting graphs.
This is my code:
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);
figure
title('Plots of U versus x')
ylabel('U(x)')
xlabel('x')
drawnow
hold on
for i=1:9
n = n+0.1;
sol = bvp4c(@(x,y)VK(x,y,n),@VKbc,sol);
plot(sol.x,sol.y(1,:));
end
hold off
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
My problem is:
1) I have to plot c aginst x.
Where:
c = (y(4)^2+y(5)^2)^((1-n)/(n+1))
How should I write the code? 2) I also have to plot U', V' and W', all aginst x. Where, (as from the code)
y(1)'= U'=c*y(4),
y(2)' = V'=c*y(5),
y(3)' = W'=-2*y(1) - a*c*y(4).
I hope someone can help me regarding this. Thank you in advance.
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Accepted Answer
Star Strider
on 23 Jan 2016
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.
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