How to solve a matrix of two symbolic variables using in-built function ode113??

1. I have a matrix B_mat of order (n+1,n+1), whose elements are computed by integrating functions of z variable.
2. I have a matrix E_mat whose elements are functions of x only, after integrating with respect to z.
3. F_mat = inv(B_mat) *E_mat
4. Y is a vector of unknown variables and
5. Fxy_mat = F_mat*y;

I am solving this Fxy_mat with ode113 in my code but didn't get success.

[Torsten]

It would be easier to follow if you directly present the ODE system you are trying to solve and the problems you encounter.

Best wishes

Torsten.

[Anu Gupta]

Thank you Torsten for your quick response!

Since the ode system is constructing in the program, I am attaching the MATLAB code Query.m

When I run this program, I got the following errors:

Error using odearguments (line 110) Inputs must be floats, namely single or double.

Error in ode113 (line 113) [neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

Error in Query (line 81) sol=ode113( @(x,y) Fxy_mat,[0 1],A_initial,odeset('abstol',1e-7,'reltol',1e-7));

Answer 1

[Walter Roberson]

You do not solve matrices of symbolic variables using ode113. The ode* functions are only for numeric work.

If you have symbolic differential equations that you want to simulate numerically, then follow the steps at odeFunction()

[Anu Gupta]

Thank you so much Walter Roberson!

Can you solve system of 100 symbolic differential equations using odeFuctions()?

[Walter Roberson]

The limit for the steps shown for odeFunction are memory and time. The step that concerns me the most in that respect is the step

f = M\F;

which I worry could be quite expensive for larger systems. In the example given in the documentation, M is essentially just a permutation matrix with a negation thrown in; those are not difficult to handle with a small program, but I worry about the general operation.

[Anu Gupta]

okay. When I use

>>ode15s(Fxy_vec,[x; y], [0 10], A_initial)

Then, also the same error comes:

Undefined function 'exist' for input arguments of type 'sym'.

[Walter Roberson]

The Fxy_vec should be the result of using odeFunction, and the timespan [x;y] should be numeric values, not symbolic values. It would be much more typical to have the times in a row vector than in a column vector; I would need to check to see if using a column vector tspan is permitted. The initial values [0 10] you have given as a row vector; note that those will become a column vector when passed in to the function, but passing a row vector here is common and permitted. A_initial is in the options slot; ode15s is going to check whether it is a struct or not, and if it is not a struct is going to treat it as an extra parameter to pass to the function.

I would suggest to you that you missed a step:

ode15s( odeFunction(Fxy_vec, [x;y]), [0 10], A_initial )

[Anu Gupta]

Actually, I am using 2014 version of MATLAB. In which, if I use the following commands:

odefun = odeFunction(Fxy_vec, [x ; y]);

ode15s(odefun, [0 10], A_intial);

Following error comes:

Undefined function 'odeFunction' for input arguments of type 'sym'.

Error in check (line 116)

odefun = odeFunction(Fxy_vec,[x; y]);

[Walter Roberson]

odeFunction was added in R2015a. Time for you to upgrade.

[Anu Gupta]

ok, thank you so much Walter Roberson for your kind help.

[Anu Gupta]

I have downloaded the 2017 version of MATLAB. But still, I am facing the problem with "odeFunction". (These two lines are followed by the above Matlab script "Query.m")

odefun = odeFunction(Fxy_vec, vars);

ode15s(odefun, [0,1], A_initial)

Error using mupadengine/feval (line 166)

Variables must be specified by univariate function calls.

Error in sym/odeFunction (line 118)

A = feval(symengine, 'daetools::odeFunction', expr, vars, params{:});

Error in odefn (line 123)

odefun = odeFunction(Fxy_vec, vars);