# BVP4c error. Would anyone help to find any error and correct this ?

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Md Sojib on 15 Apr 2024
Answered: Ayush Anand on 15 Apr 2024
%𝑦"= 𝑦 ̇^2/2𝑟+𝑠𝑖𝑛𝑦/𝑟+(y'cosy)/𝑟+ 2/𝜆^2 (siny) −(y/𝑟)r' -cosy/r;
%where 𝜆 is constant
% r'=cosy
%h'=siny
% Boundary conditions: r(0)=Rsin(alpha), h(0)=Rcos(alpha), y(0)=alpha,
% y(inf)=0, y'(inf)=0
R = 10.2e-9;
sc = 390e-18;
solinit = bvpinit(linspace(-10,10,50),@init_guess);
sol = bvp5c(@f1, @bc1, solinit);
%options = bvpset('RelTol', 1e-8, 'states', 'on');
function dydx=f1(x,y)
y1=y(1); %y
y2=y(2); %r
y3=y(3); %h
y4=y(4); %y'
y2p=cos(y1);
y3p=sin(y1);
ypp=(y4^2)/(2*y2)+sin(y1)/y2+y4*cos(y1)/y2+(2/1.8e-9^2)*y3-y1*y2p/y2-cos(y1)/y2;
dydx=[y4;y2p;y3p,ypp];
end
function res=bc1(y0,yinf)
R=10.2e-9;
sc=390e-18;
alpha = (1/(2*pi*R^2)-sc)*(sc*sqrt(4*pi*R^2)-sc);
res=[y0(2)-R*sin(alpha); y0(3)+R*cos(alpha); y0(1)-alpha; yinf(1); yinf(4)];
end
function guess = init_guess(x)
guess = [pi-x/20,sin(x/20),x,0];
end

Ayush Anand on 15 Apr 2024
Hi,
You need to replace the comma before ypp with a semi-colon to create a 4-column vector
%Replace dydx=[y4;y2p;y3p,ypp]; with
dydx=[y4;y2p;y3p;ypp];
Also, you have a 4-column vector defined as the output of "f1" , and the system is a 4th order differential, while there are 5 boundary conditions defined as the output of "bc1" . You will need to remove one of the boundary conditions for the dimensions to match with "f1", as "bvp5c" expects the number of boundary conditions to match the order of the differential.