How to apply asymptotic matching condition in bvp4c?
1 view (last 30 days)
Show older comments
Hi, I want to know how to write the code to apply asymptotic matching condition? In the paper, it is stated that they apply asymptotic matching condition for the range of 0.5<n=<1. The asymptotic matching condition is,
(U'(x),V'(x))=(n/(x*(n-1)))*(U(x),V(x)) as x->infinity
This is the code without the asymptotic condition.
function ScriptAA
n=0.5;
infinity=20;
solinit = bvpinit(linspace(0,infinity,30),[0 1 0 -1 0]);
sol = bvp4c(@(x,y)VK(x,y,n),@VKbc,solinit);
x = [0:2:20];
y = deval(sol,x);
figure
plot(sol.x,sol.y(1,:)); %Plot U,V,W,Theta
title('Plots of U versus x')
ylabel('U(x)')
xlabel('x')
drawnow
hold on
for i=2:6
n = n+0.1;
sol = bvp4c(@(x,y)VK(x,y,n),@VKbc,sol);
lines = {'b-','c-','r-','g-','k-','y-'};
plot(sol.x,sol.y(1,:),lines{i}); %Plot U,V,W,Theta
end
legend('n = 0.5, n = 0.6','n = 0.7','n = 0.8','n = 0.9','n = 1.0',1);
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));
b = ((c*y(4))^2+(c*y(5))^2)^((n-1)/2);
yprime = [ c*y(4) % U'
c*y(5) % V'
-2*y(1) - a*c*y(4) % W'
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
Thank you in advance!
0 Comments
Answers (0)
See Also
Categories
Find more on Partial Differential Equation Toolbox in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!