Find difficult in solving these four coupled ODE's using ODE45....I have attached a file regarding these equations..

function dy=pair(t,y,a,b,d,hstress,sigma,Hstar,kc,c) 
dy(1)=  a*sinh((b*(sigma^d)*(1-y(2)))/((1-y(3))*(1-y(4)))) ;
dy(2)=((hstress*(a*sinh(b*(sigma^d)*(1-y(2)))/(1-y(3))*(1-y(4))))/(sigma^d))*(1-y(2)/Hstar);
dy(3)=(kc/3)*power((1-y(3)),4);
dy(4)=  c*y(1);
dy=dy';
end
Error
>> a=0.5179;
>> b=1.1003E-3;
>> c=0.4576;
>> d=1;
>> hstress=3463.46;
>> Hstar=0.7846;
>> Kc=0.1137;
>> tspan=0:0.01:40;
 pair
Error using pair (line 3)
Not enough input arguments.
 
>> pair
Error using pair (line 3)
Not enough input arguments.
 
>> [t,y]=ode45(@pair,tspan,[0 0 0 0 0]);

I suspect I know a bit of what's going wrong, yet I'm at a loss for how to fix it. Any help is much appreciated!

Answer 1

[madhan ravi]

 a=0.5179;
 b=1.1003E-3;
 c=0.4576;
 d=1;
 hstress=3463.46;
 Hstar=0.7846;
 Kc=0.1137;
 tspan=0:0.01:40;
 initial_conditions=[0;0;0;0]  %change the intial condition according to your values
 [t,y]=ode45(@(t,y)pair(t,y,a,b,d,hstress,sigma,Hstar,Kc,c),tspan,initial_conditions)   %function call
 plot(t,y(:,1))
 
function dy=pair(t,y,a,b,d,hstress,sigma,Hstar,kc,c)           %function definition
dy=zeros(4,1);
dy(1)=a*sinh((b*(sigma^d)*(1-y(2)))/((1-y(3))*(1-y(4)))) ;
dy(2)=((hstress*(a*sinh(b*(sigma^d)*(1-y(2)))/(1-y(3))*(1-y(4))))/(sigma^d))*(1-y(2)/Hstar);
dy(3)=(kc/3)*power((1-y(3)),4);
dy(4)=c*y(1);
end

[ruban ramalingam]

I am getting an error.." function definitions are permitted are in this context"..

Please reply how to fix this error..

[Walter Roberson]

store the code from the function line onwards in pair.m

[madhan ravi]

Just do what sir Walter says or copy the whole answer and paste it in a script , save it and run it

[Walter Roberson]

putting everything into aa script requires r2016b or later which II suspect the user does not have .

[madhan ravi]

yes sir Walter I agree , @Ruban save the function as pair.m(same name of the function) and try the rest of the code in a separate file , this will get you to the solution.

[ruban ramalingam]

First of all, thank u so much for your help...

Last thing..

Code is working as per you said... But one thing

it runs for only t=10; even tspan is given upto 40...

Even if we increases the tspan, it plots the curve only upto 10...

What could be the error??

I attached the snapshot which I got in the matlab?? please find the attachment.

[madhan ravi]

no everything is alright see my attached picture in my answer , the x-axis represents the time

[ruban ramalingam]

Sorry sir to disturb you..

The same error continues.. The curve shows upto t=10..

Even I tried with higher version (MATLAB 2018a)..

and which version of MATLAB you are using ??

Even in the program, you didn't give the input of sigma =180; but it is running for you...

Please help me to sort out this error?

[Walter Roberson]

Warning: Failure at t=9.795692e+00.  Unable to meet integration tolerances without reducing the step size below the smallest value allowed (2.842171e-14) at time t. 
> In ode45 (line 360) 

[Walter Roberson]

y(4) goes to 1. You have

dy(1)=a*sinh((b*(sigma^d)*(1-y(2)))/((1-y(3))*(1-y(4)))) ;

so 1-y(4) goes to 0, and that is a denominator so dy(1) goes to infinity.

[ruban ramalingam]

Is the function wrong sir ?? as per your comments sir..