How do you make an initial guess in bvp4c?
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Marcus Rosales
el 5 de Feb. de 2024
Comentada: Marcus Rosales
el 6 de Feb. de 2024
I am trying to sovle the following differential equation using bvp4c:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1608566/image.png)
There are issues at the origin... I need to solve here though!
In certain limits you can say
, so I would like to guess this as an initial solution. I tried something like this (xl=0, xr=100 or so):
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1608571/image.png)
function [Sxint, xint] =bvp4c_mathworks_Abrikosov_guess(xl,xr)
N = 5000;
xint = linspace(xl,xr,N);
solinit = bvpinit(xint,@guess);
sol4c = bvp4c(@myode,@mybc,solinit);
Sxint = deval(sol4c,xint);
end
function dy = myode(r,y)
k = 5/sqrt(2);
dy(1,1) = y(2);
dy(2,1) = k^2*(y(1)^2-1)*y(1)+y(1)/r^2-y(2)/r;
end
function res = mybc(ya,yb)
res = [ya(1)
yb(1)-1];
end
function g = guess(x)
k = 5/sqrt(2);
g = tanh(x/k);
end
Is there a way to do this? What do I need to change?
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Respuesta aceptada
Torsten
el 5 de Feb. de 2024
Editada: Torsten
el 5 de Feb. de 2024
xl = 1e-8;
xr = 5;
[Sxint, xint]=bvp4c_mathworks_Abrikosov_guess(xl,xr);
plot(xint,Sxint(1,:))
hold on
M = cell2mat(arrayfun(@(x)guess(x),xint,'UniformOutput',0));
plot(xint,M(1,:))
hold off
function [Sxint, xint] =bvp4c_mathworks_Abrikosov_guess(xl,xr)
N = 500;
xint = linspace(xl,xr,N);
solinit = bvpinit(xint,@guess);
sol4c = bvp4c(@myode,@mybc,solinit);
Sxint = deval(sol4c,xint);
end
function dy = myode(r,y)
k = 5/sqrt(2);
dy(1,1) = y(2);
dy(2,1) = k^2*(y(1)^2-1)*y(1)+y(1)/r^2-y(2)/r;
end
function res = mybc(ya,yb)
res = [ya(1)
yb(1)-1];
end
function g = guess(x)
k = 5/sqrt(2);
g = [tanh(x/k);1/k*(1-tanh(x/k)^2)];
end
3 comentarios
Torsten
el 5 de Feb. de 2024
Yes, you solve for f and f', and you have to specify initial profiles for both of them.
So if you specify f0 = tanh(x/k) as initial guess for f, it's natural to use f0' = 1/k*(1-tanh(x/k)^2) as initial guess for f'.
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