I am trying to plot the real part and imaginary part graph using bvp4c and I am getting a straight line,

I have a coupled non-linear differential equations

(d^2 f)/(dy^2 )+m2*g2*dB/dy-2*i*R2*g1*f - g3*G1*y - R4*g1 = 0

(d^2 B)/(dy^2 )+t4/(1-i*H1)*df/dy=0

Boundary conditions are

f=0 at y=0

f=C1 at y=1

And

dB/dy-(t4/(P1* (1-i*H1 ) ))* B=0 at y=0

dB/dy+(t4/(P2 (1-i*H1 ) ))* B=0 at y=1

Matlab programs

close all

clc

p=1;
P1=2;
P2=2;
b1=0.00021;
b2=0.000058;
S1=0.005;
S2=580000;
G1=2;
m2=20;
R1=997.1;
R2=3;
C1=1;
R3=4420;
B=0.5;
H1=0.25;
K1=3;
R4=1;
t1=(1./((1-p).^2.5));
t2=(1-p)+(p.*(R3./R1));
t3=(1-p)+p.*((R3.*b2)./(R1.*b1));
S=(S2./S1);
t4=1-((3*(1-S).*p)./((2+S)+(1-S).*p));
g1=t2./t1;
g2=1/t1;
g3=t3./t1;
m1=(t4./(P1.*(1-1i.*H1)));
m2=(t4./(P2.*(1-1i.*H1)));
dydx=@(x,y)[y(3);
    y(4);
    -m2.*g2.*y(4)+2.*1i.*R2.*g1.*y(1)+g3.*G1.*x+R4.*g1;
    (-t4./(1-1i.*H1)).*y(3)];
BC = @(ya,yb)[ya(1);yb(1)-C1;ya(4)-m1.*ya(2);yb(4)+m2.*yb(2)];
yinit = [0.01;0.01;0.01;0.01];
solinit = bvpinit(linspace(0,1,50),yinit);
U1 = bvp4c(dydx,BC,solinit);       
hold on
plot(U1.x,real(U1.y(1,:)),'r','linewidth',1.5)
plot(U1.x,imag(U1.y(1,:)),'b','linewidth',1.5)

I am trying to plot the real part and complex part graph and I am getting a straight line, I have checked the program and it seems good, but the type of graph I need to get is not appearing, I think the bvp4c code I have written might be wrong. Please help me. The graph I have to get should be of the form. Thank you

[Torsten]

Your boundary condition is f = 1 at y=1. Thus the correct solution cannot look like the one you included.

[Syed Mohiuddin]

If the boundary condition is f=C1=0 at y=1, then i have to get the graph of the form, but i am getting just a single straight line, i am not even getting real and complex part of the graph. I cannot figure out where I have made the mistake, please help. Thank you

[Torsten]

m2 and t4 are extremely large numbers. Are you sure they are correct ?

In the settings for bvp4c, I cannot find an error.

[Syed Mohiuddin]

I followed your suggestion and have checked the values of m2 and t4, they are correct, but i think because i took p=1, therefore t1 tends to infinite value, but if i take p=2 and C1=0, then the graph is different, but still their is an error in the graph near the boundaries.

[Syed Mohiuddin]

I have got the solutions, thank you very much. Great suggestion

[Torsten]

And what was the problem ?

[Syed Mohiuddin]

By taking p=0.1 and C1=0, i got the required graph. Thanks a lot

[Syed Mohiuddin]

I need to accept this answer also, please provide an option to accept. Thank you