Finding difficult to solve this coupled ode equations using ode45

I have been solving this two coupled ODE equations using ode45... Please find the attached files....

Even after defining the variable 'P'...,

I am getting an error

Undefined

function or

variable 'P'.

Error in

pair1 (line

5)

dy(1)=(P*(b^2)*v*sigma_e*((y(2)^2*sigma_e).^(-1/3))/(M^2))*exp(-Q/K*T)*sinh((sigma_e)/((M*K*T)*(b^3))*(Q/((y(2)).^2*sigma_e)).^(1/3));

Error in

@(t,y)pair1(t,y)

Error in

odearguments

(line 87)

f0 =

feval(ode,t0,y0,args{:});

% ODE15I sets

args{1} to

yp0.

Error in

ode45 (line

113)

[neq, tspan,

ntspan, next,

t0, tfinal,

tdir, y0, f0,

odeArgs,

odeFcn, ...

Error in

ruban (line

13)

[t,y]=ode45(@(t,y)pair1(t,y),tspan,initial_conditions)

%function

call

Please help me to sort out this problem by modifying the code or providing the hints...

Any help will be appreciated

Answer 1

[madhan ravi]

Parameterize your function as below:

 P=10E12;
 b=0.268E-9;
 Q=285;
 M=3;
 K=1.38E-23;
 v=3.6E16;
 sigma_e=200;
 T=923;
 ec=0.04;
 c=7; %provide your value
 tspan=0:0.01:70;
 initial_conditions=[0.01,100]; %change the intial condition according to your values
 [t,y]=ode45(@(t,y)pair1(t,y,P,Q,b,c,v,sigma_e,M,K,T,c,ec),tspan,initial_conditions)   %function call
 plot(t,y(:,1))
 
 
function dy=pair1(t,y,P,Q,b,c,v,sigma_e,M,K,T,c,ec)           %function definition
dy=zeros(2,1);
dy(1)=(P*(b^2)*v*sigma_e*((y(2)^2*sigma_e).^(-1/3))/(M^2))*exp(-Q/K*T)*sinh((sigma_e)/((M*K*T)*(b^3))*(Q/((y(2)).^2*sigma_e)).^(1/3));
dy(2)=(1/(y(2)*ec))*((c^2)-(y(2))^2)*y(1);
end

[ruban ramalingam]

I am getting an error like this..

Function definitions are not permitted in this context...

What to do to sort out this..

[ruban ramalingam]

Are u getting any plot?? Please show the plot..

I am getting the same error like this..

Function definitions are not permitted in this context...

[ruban ramalingam]

Error using pair1
Too many input arguments.

Error in @(t,y)pair1(t,y,P,Q,b,c,v,sigma_e,M,K,T,c,ec)

Error in odearguments (line 87)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

Error in ode45 (line 113)
[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

Error in sunny (line 13)
[t,y]=ode45(@(t,y)pair1(t,y,P,Q,b,c,v,sigma_e,M,K,T,c,ec),tspan,initial_conditions)
%function call 

[madhan ravi]

let me get back in a few minutes debugging it..

Answer 2

[madhan ravi]

Corrected equations , please clarify if something is not clear:

% y(1)=>epsilon
% y(2)=>sigma
%dy(1)=>equation2
%dy(2)=>equation1
dy(1)=(1./(y(2)*epsilon_c))*(sigma_is.^2-y(2).^2)*y(1);
dy(2)=((rho_m.*b.^2.*V_D.*sigma_e.*(y(2).^2.*sigma_e).^(-1/3))...
./M.^2).*exp(-Q/R.*T).*(sinh(sigma_e/(M*K*T).*b.*(G/(y(2).^2.*sigma_e).^(1/3))));

[ruban ramalingam]

Sorry sir for the late response...

Still getting the same error..

Please find the attached files...

[ruban ramalingam]

I am ending with this following error... Please help me to sort out this error

Error using pair1
Too many input arguments.

Error in @(t,y)pair1(t,y,P,Q,b,c,v,sigma_e,M,K,T,c,epsilon_c)

Error in odearguments (line 87)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

Error in ode45 (line 113)
[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs,
odeFcn, ...

Error in sunny (line 14)
[t,y]=ode45(@(t,y)pair1(t,y,P,Q,b,c,v,sigma_e,M,K,T,c,epsilon_c),tspan,initial_conditions)
%function call

[madhan ravi]

Ruban Ruban slow down.. alright! first verify the equations properly in this answer with lates equations that you attached.

[ruban ramalingam]

Sorry sir..

y(1) should be sigma..

y(2) should be epsilon sir...

Please see the attached equations

[madhan ravi]

To avoid confusions further let me rephrase.

• Please see this answer (the equations) and create a pdf with all the necessary details (meaning the datas) of the variables according to the answer provided.
• Let know of the intial conditions.
• Let know of the time span.
• Upload the latex form of the equations which is elligible to read unlike now.

If you fulfill all the above requirements then a well suitable solution can be attained sooner than expected.

[ruban ramalingam]

Sir,

Do you need the article?? ..

I attached that article having necessary details which I tried to implement... Please see the article..

Another thing

Typically I ended with this error whenever I am trying to solving any ode equations using ode45.. I am not clear with the syntax of ode45.. Eventually I want to optimising the variables using optimisation toolbox..

Error in odearguments (line 87)

f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 113)

[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs,

odeFcn, ...

Will you help me in understanding this??

I am not clear with the syntax of ode45.. Eventually I want to optimise the variables using optimisation toolbox..