## Increasing number of points bvp4c

### pxg882 (view profile)

on 26 Nov 2012

I'm running the following script

function M = SwirlingFlow(~)

M = bvpinit(linspace(0,20,241),@VKinit);
options = bvpset('RelTol',1e-6);
sol = bvp4c(@VK,@VKbc,M,options);

figure;
hold all;
plot(sol.x,sol.y(2,:));
plot(sol.x,sol.y(4,:));
hold off;
xlabel('\zeta')
xlabel('\zeta')
hleg = legend('F\prime','G\prime','Location','NorthEast'); %#ok<NASGU>

figure;
hold all;
plot(sol.x,sol.y(1,:));
plot(sol.x,sol.y(3,:));
plot(sol.x,(-1)*sol.y(5,:));
hold off;
xlabel('\zeta')
hleg = legend('F','G','-H','Location','East'); %#ok<NASGU>

disp('Value of F''(0)')
a = sol.y(2,1);
disp(a)

disp('Value of G''(0)')
b = sol.y(4,1);
disp(b)

disp('Value of H(infinity)')
c = sol.y(5,end);
disp(c)

function yprime = VK(~,y)

yprime = [  y(2)
y(1)^2 - y(3)^2 + y(2)*y(5)
y(4)
2*y(1)*y(3) + y(4)*y(5)
-2*y(1)];

function res = VKbc(ya,yb)

res = [ya(1);ya(3)-1;ya(5);yb(2)-(yb(5)*yb(1));yb(4)-(yb(5)*yb(3))];

function yinit = VKinit(~)

yinit = [0;0.510233;1;-0.615922;0];


However the solution only converges to the correct solution using 241 integration points or less. Anything greater than this and the solution diverges from the true solution. Does anybody know how I would be able to increase the number of points whilst still producing the true solution?

Thanks.