How should i go about solving a set of ODEs for a set of data points? I would like to automate it as much as possible.

Currently I am using the ode45 solver, with my input parameters being a vector of length 7, which is two separate terms being length 6 and 1. My equations has a variable which needs to be solved for set amount of time and then it changes.

How do i go about doing this?

%so what im doing is,
tspan = [0 20];
options = odeset('MaxStep',0.05,'RelTol',1e-8,'AbsTol',1e-9);
stress1 = [525 450 385 200 150];
stress2 = [630 560 475 332 200];
for ii =1:length(stress1) % i intend to repeat this process for stress2
odeIp = [0 0 0 0 0 0 0 1 ii]';
odeOp = ode45(@odefn,tspan,odeIp,options);
Var2 = odeOp( : , 7); %gives me Solrequired
VarRequied(:,ii) = Var2;
end
%in the function im im using If statement to choose my initial conditions
function dOdeOp = odefn(t,odeIp)
%input constants and splitting the terms
stress1 = [525 450 385 200 150];
stress2 = [630 560 475 332 200];
D0 = odeIp(7,1);
alpha = odeIp(1:6);
var = odeIp(8,1);
sigvar = odeIp(9,1);
if var ==1
    mSig = 0;
else
    mSig = 100;
end
if var ==1
    aSig = stress1(sigvar);
else
    aSig = stress2(sigvar);
end
equat = mSig + aSig*sin(omega*t);
dequat = aSig*omega*cos(omega*t);
%solve set of equations outputs Sol1,SolRequired
% solving a bunc of equtions to get Sol1 which is an array of 1x6 and SolRequired
% which makes up the 7 column
dOdeOp1 =[Sol1;SolRequired];
dOdeOp2 = [dOdeOp1;var];
dOdeOp = [dOdeOp2;sigvar];

currently only the last two coulmns of my output vector is obtaining values, which shouldnt be the case

Answer 1

[Jon]

Please see my earlier comments.

From the behavior you describe, it looks like Sol1 and SolRequired are returned empty from what ever solver produces them. In that case your last few lines of code would result in a dOdeOp that has only two elements (var and sigvar).

[Jon]

When I run your code I get the error

Array indices must be positive integers or logical values.

Error in odequest>ContinuousAlp (line 49)

sigmaA = sigmaMean100(sigvar);

Error in ode45 (line 299)

f2 = odeFcn_main(t2, y2);

Error in odequest (line 17)

[t,alphaD]= ode45(@ContinuousAlp,tspan,alphaD0,options);

Stepping through with the debugger, I see this is caused by the fact that you are assuming that alphaD0 will always be an integer. Note that since ode45 is free to adjust this value as it iterates, it reassign this value as:

K>> alphaD0

alphaD0 =

0

0

0

0

0

0

0

1.0040

1.0040

Note that now the last two elements are not integers, so your later lines of code

sigvar = alphaD0(9,1);
.
.
.
 sigmaA = sigmaMean100(sigvar)

Have an error, because the index to sigmaMean100 must be an integer, and it is 1.0040

[Sajjan Gundmi Satish]

i get it now, but how should i prevent ode45 changing the value as it iterates?

[Jon]

I think it is fundamental to the nature of numerically solving ode's such as dy/dt = f(y), that you need the ability to evaluate the derivative for a range of possible y values.

I think instead you must rethink your logic inside of your function that provides the derivative so that it properly evaluates the derivative for what ever y value is supplied.

Although you will have to work out the details I think the basic strategy for covering your various cases is to have a function that evaluates dy/dt for any value of y. Then within your loop, you select and assign local variable (which can be accessed by your dy/dt function) which define the appropriate inputs for each pass (value of ii) and then call ode45

[Sajjan Gundmi Satish]

Thank You so much, this was very insightful.

[Jon]

Glad it was helpful. Good luck with your project!

Answer 2

[Jon]

I am not clear on the details of your implementation. It would take some time to go through it all line by line.

In case it is helpful though I noticed a couple of things that could be problematic.

I don't see where you ever use the values that you have assigned to the variable that you have named "variable". As a side point, it would make your code more understandable if you used a more descriptive name than "variable".

I don't see where you ever assign a value to Dataset1 and Dataset2

I don't see where you ever assign a value to SolRequired

The variables equat and dequat never seem to be used

[Sajjan Gundmi Satish]

Hey thank you for your comment, i have made some edits hopefully it is easier to understand now. Basically i hve to run the function for 20 second for each of the value in stress1 and gives me the SolRequired, which i try to store as VarRequied. There more equations which i havent mentioned which uses equat1 and dequat.

[Jon]

So just to be clear, your problem is that values are only being assigned to the last two elements of odeOp?

If you could make a self contained example script that demonstrates the problem, then I can run then I might be able to step through and see what is wrong.

Even better, I would suggest that you single step through your code using the MATLAB debugging tools, and then you can see exactly what is happening. At each step you can see the values of the various variables, and also how it is following the branching logic. If you are not already familiar with how to use the MATLAB debugging tools, I highly recommend learning about them. Check out https://www.mathworks.com/help/matlab/matlab_prog/debugging-process-and-features.html

[Jon]

Sorry, I inadvertently opened up a second answer to this question rather than continuing the original thread. They both however go together.