I have matlab code, when i run the program i could 't get the values and also graph.Can u help me in this regards?

Here, i have attached my program.

[Mathieu NOE]

not really....

[sunitha kolasani]

%d^2f/dy^2+n1*A1*df/dy+M1*A2*dh/dy+(2*i*k1*A1-(i/k))*f+A3*G1*y(1)+A4*G2*y(3)=0
%A5*(1+i*m)* d^2h/dy^2+df/dy+n1*P2*dh/dy=0.
%Boundary conditions are: f=1,h=M at y=0 and df/dy, dh/dy=0 as y=infinity.


close all
clc
b1 = 0.5;
f1 = 0.5;
k = 0.3;
k1 = 0.5;
H1 = 0.2;
M = 1;
M1 = 16;
n1 = 0.25;
p1 = 6.2;
p2 = 0.7;
S1 = 1;
P11 = 0.02;
Sd = 0.78;
m = 0.5;
G1 = 4;
G2 = 5;
d1 = (1./((1-P11).^2.5));
R1 = 4420;
C1 = 0.56;
C11 = 4179;
R11 = 997.1;
d2 = ((1-P11)+P11.*(R1./R11));
B1 = 0.000058;
B11 = 000021;
d3 =(1-P11)+P11.*((R1.*B1)./(R11.*B11));
Be1 = 0.006;
Be2 = 1;
d4 = (1-P11)+P11.*((R1.*Be1)./(R11.*Be2));
si1 = 580000;
si2 = 0.005;
si=(si1./si2);
d5 = 1-((3.*(1-si).*P11)./((2+si)+(1-si).*P11));
Ro1 = ((R1.*C1)./(R11.*C11));
d6 = ((1-P11)+(P11.*Ro1));
Kf = 0.613;
Ks = 7.2;
K = (Kf./Ks);
d7 = ((1+2.*P11)+2.*(1-P11).*K)./((1-P11)+(2+P11).*K);
A1 = (d2./d1);
A2 = (1./d1); 
A3 = ((d2.*d3)./d1); 
A4 = ((d2.*d4)./d1); 
A5 = (1./d5);
A6 = (d6./d7);
A7 = (1./d7); 
A8 = (1./1-P11);
dydx = @(x,y)[y(6);
    y(8);
    -(M1*A2*y(8))-(2.*1i.*k1.*A1-(1./k).*y(5))-n1.*A4.*y(6)-G1.*y(1).*A6-G2.*y(3).*A7;
    -(1./(1+1i.*m).*A3).*y(6)-(n1.*P2./(1+1i.*m)).*y(8)];
BC = @(ya,yb)[ya(5)-1;yb(6)-0;ya(7)-M;yb(8)-0];
yinit = [0.01;0.01;0.01;0.01;0.01;0.01;0.01;0.01];
solinit = bvpinit(linspace(0,1,50),yinit);
options = bvpset('AbsTol',1e-3);
f = bvp4c(dydx,BC,solinit,options);

Unrecognized function or variable 'P2'.

Error in solution>@(x,y)[y(6);y(8);-(M1*A2*y(8))-(2.*1i.*k1.*A1-(1./k).*y(5))-n1.*A4.*y(6)-G1.*y(1).*A6-G2.*y(3).*A7;-(1./(1+1i.*m).*A3).*y(6)-(n1.*P2./(1+1i.*m)).*y(8)] (line 57)
-(1./(1+1i.*m).*A3).*y(6)-(n1.*P2./(1+1i.*m)).*y(8)];

Error in bvparguments (line 96)
testODE = ode(x1,y1,odeExtras{:});

Error in bvp4c (line 119)
bvparguments(solver_name,ode,bc,solinit,options,varargin);

hold on

plot(f.x,real(-[f.y(5,:)]),'b','linewidth',1.5)
plot(f.x,imag([f.y(5,:)]),'b','linewidth',1.5,'linestyle','--')

[sunitha kolasani]

This is my program.

[Torsten]

You have two 2nd order order differential equations, thus four 1st order differential equations to solve.

Thus the y-values should run between y(1) and y(4) and not between y(1) and y(8) and you should have 4 instead of 8 initial values.

[sunitha kolasani]

Actually i have total 4 equations.

[Sam Chak]

@sunitha kolasani, Do you mean these four?

[Torsten]

Four 2nd order equations ? You only implemented two of them: the one for f and the one for h.

Answer 1

[Torsten]

Don't solve the equations separately (first for T and C, then for f and h) , but all four together in one call to bvp4c.

They are coupled all together.

Answer 2

[Ronit]

Hello Sunitha,

After executing the program, the error message indicates that the function dydx and BC are not returning the column vector of the correct length 8 to match the number of differential equations. To fix this you can try the following approach:

(Assuming P2 used in dydx is p2)

dydx = @(x,y)[y(2);
              y(4);
              y(6);
              y(8);
              -(M1*A2*y(8))-(2*1i*k1*A1-(1/k))*y(5)-n1*A4*y(6)-G1*y(1)*A6-G2*y(3)*A7;
              y(7);
              -(1/(1+1i*m)*A3)*y(6)-(n1*p2/(1+1i*m))*y(8);
              y(5)];

BC = @(ya,yb)[ya(1)-1; % f = 1 at y = 0
              ya(3)-M; % h = M at y = 0
              yb(2);   % df/dy = 0 as y -> infinity
              yb(4);   % dh/dy = 0 as y -> infinity
              ya(2);   % Initial condition for df/dy
              ya(4);   % Initial condition for dh/dy
              yb(6);   % Additional condition for df/dy
              yb(8)];  % Additional condition for dh/dy

Please go through this post for better understanding on using bvp4c to find derivative: https://www.mathworks.com/matlabcentral/answers/1863463

Regards!

[sunitha kolasani]

%d^2f/dy^2+n1*A1*df/dy+M1*A2*dh/dy+(2*i*k1*A1-(i/k))*f+A3*G1*y(1)+A4*G2*y(3)=0, -Equation1

%A5*(1+i*m)* d^2h/dy^2+df/dy+n1*P2*dh/dy=0, Equation-2
%The above 2 are coupled equations
%Boundary conditions are: f=1,h=M at y=0 and df/dy, dh/dy=0 as y=infinity.

%next 2 equations I have solved separately because these 2 are also coupled

%d^2T/dy^2+n1*p1*A6*dT/dy-S1*p1*A7*T=0, Equation-3
%d^2C/dy^2+n1*Sd*A8*dC/dy-H1*sd*A8*C=0, Equation-4
%Boundary conditions are: dT/dy=A7*b1*(T-1), dC/dy=f1*A8*(C-1) at y=0.
%  T,C=0 at y=infinity.
%First I have written the code for “T” and “C” next separate program written for first 2 eqations:
%The below code is for first 2 equations:

close all
clc
b1 = 0.5;
f1 = 0.5;
k = 0.3;
k1 = 0.5;
H1 = 0.2;
M = 1;
M1 = 16;
n1 = 0.25;
p1 = 6.2;
p2 = 0.7;
S1 = 1;
P11 = 0.02;
Sd = 0.78;
m = 0.5;
G1 = 4;
G2 = 5;
d1 = (1./((1-P11).^2.5));
R1 = 4420;
C1 = 0.56;
C11 = 4179;
R11 = 997.1;
d2 = ((1-P11)+P11.*(R1./R11));
B1 = 0.000058;
B11 = 000021;
d3 =(1-P11)+P11.*((R1.*B1)./(R11.*B11));
Be1 = 0.006;
Be2 = 1;
d4 = (1-P11)+P11.*((R1.*Be1)./(R11.*Be2));
si1 = 580000;
si2 = 0.005;
si=(si1./si2);
d5 = 1-((3.*(1-si).*P11)./((2+si)+(1-si).*P11));
Ro1 = ((R1.*C1)./(R11.*C11));
d6 = ((1-P11)+(P11.*Ro1));
Kf = 0.613;
Ks = 7.2;
K = (Kf./Ks);
d7 = ((1+2.*P11)+2.*(1-P11).*K)./((1-P11)+(2+P11).*K);
A1 = (d2./d1);
A2 = (1./d1); 
A3 = ((d2.*d3)./d1); 
A4 = ((d2.*d4)./d1); 
A5 = (1./d5);
A6 = (d6./d7);
A7 = (1./d7); 
A8 = (1./1-P11);
dydx = @(x,y)[y(2);
    y(4);
    y(6);
    -(M1*A2*y(8))-(2.*1i.*k1.*A1-(1./k).*y(5))-n1.*A4.*y(6)-G1.*y(1).*A6-G2.*y(3).*A7;%First equation
    y(8);
    -(1./(1+1i.*m).*A3).*y(6)-(n1.*p2./(1+1i.*m)).*y(8)];%second equation
BC = @(ya,yb)[ya(5)-1; %f=1 at y=0 
    yb(6)-0;% df/dy=0 as y=infinity 
    ya(7)-M; %,h=M at y=0
    yb(8)-0];% dh/dy=0 as y=infinity
yinit = [0.01;0.01;0.01;0.01;0.01;0.01;0.01;0.01];
solinit = bvpinit(linspace(0,1,50),yinit);
options = bvpset('AbsTol',1e-3);
f = bvp4c(dydx,BC,solinit,options);

Error using bvparguments (line 99)
Error in calling BVP4C(ODEFUN,BCFUN,SOLINIT,OPTIONS):
The derivative function ODEFUN should return a column vector of length 8.

Error in bvp4c (line 119)
bvparguments(solver_name,ode,bc,solinit,options,varargin);

hold on

plot(f.x,real(-[f.y(5,:)]),'b','linewidth',1.5)
plot(f.x,imag([f.y(5,:)]),'b','linewidth',1.5,'linestyle','--')

[sunitha kolasani]

I have modified my problem with little changes. Can anyone help me to find the graph.

[sunitha kolasani]

yes. first two are T and C then next two are f and h.

Do u mean in one bvp4c program i should write all 4 equations ?

[sunitha kolasani]

T =y(1), C=y(3), dT/dy=y(2), dc/dy=y(4). (These are coupled so that i have solved separately)

f=y(5),df/dy=y(6), h=y(7), dh/dy=y(8). (these two are also coupled)

[Torsten]

Do u mean in one bvp4c program i should write all 4 equations ?

Yes, because they are coupled all together.

[sunitha kolasani]

ok thank you i will write the program in that way.

[sunitha kolasani]

Where is the option to vote for you.

[Torsten]

@sunitha kolasani

Thank you for your feedback. I changed my comment to an answer for your question.