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

%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

Answer 1

[Ayush Anand]

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.

You can read more about "bvp5c" here: https://www.mathworks.com/help/matlab/ref/bvp5c.html