How to input a "sym" type equation into ODE45 to solve first order differential equation?

% Sample
close all;
clear all;
clc;

syms t tt;

a=1;
b=2;
c=3;

fs_d=50*t^2+60*t^4+70*t^9;
fd_d=diff(fs_d,t);

dTime=1e-6; % time step
Tfinal=timeduration; % time final
zeit=0:dTime:Tfinal; %

% ODE solver
% initial condition
x1_0=0;
dx1_0=0;

%ode45
options = odeset('RelTol',1.e-6);
[tt,dx] = ode45(@(tt,x) Output123(tt, x, a, b, c, fd_d, t), zeit, x1_0, options);

function dx = Output123(tt, x, a, b, c, fd_d, t)
    
    tic;
    
    %dx(1)=x(2);
    dx=-a*subs(fd_d,t,tt)*b/(c)-x*(b/(c));
        
    dx = dx'; % output result
    
    toc;
    
end

The above the a sample code I want to achieve, it is a first order differential equation, the "subs" method works for second order differential equation.

Can anyone help me with this problem?

Thanks,

Answer 1

[Star Strider]

I do not understand what you are doing.

However the correct way to use a symbolic different ia equation with the numeric solvers would be something like this —

syms a b c t tt x
fs_d=50*t^2+60*t^4+70*t^9;
fd_d=diff(fs_d,t);
f=-a*subs(fd_d,t,tt)*b/(c)-x*(b/(c))

f = 

Output123 = matlabFunction(f, 'Vars',{tt,x,a,b,c}) 

Output123 = function_handle with value:
    @(tt,x,a,b,c)-(b.*x)./c-(a.*b.*(tt.*1.0e+2+tt.^3.*2.4e+2+tt.^8.*6.3e+2))./c

a=1;
b=2;
c=3;

timeduration = 1;
dTime=1e-6; % time step
Tfinal=timeduration; % time final
zeit=0:dTime:Tfinal; %

x1_0=0;
dx1_0=0;

options = odeset('RelTol',1.e-6);
[tt,x] = ode45(@(tt,x) Output123(tt, x, a, b, c), zeit, x1_0, options);

figure
plot(tt, x)
grid

Make appropriate changes to ger the resullt you want.

.

[haohaoxuexi1]

Thank you my friend. Do you think you can write the code in a way like I did here?

function dx = Output123(tt, x, a, b, c, fd_d, t)
    
    tic;
    
    %dx(1)=x(2);
    dx=-a*subs(fd_d,t,tt)*b/(c)-x*(b/(c));
        
    dx = dx'; % output result
    
    toc;
    
end

[haohaoxuexi1]

@Star Strider

[Star Strider]

My pleasure!

Creating that as a function file is straightforward —

function dx = Output123(tt,x,a,b,c)
    dx = -(b.*x)./c-(a.*b.*(tt.*1.0e+2+tt.^3.*2.4e+2+tt.^8.*6.3e+2))./c;
end

The trest of the code remains unchanged. With only one differential equation, transposing it is not appropriate. There is no need to pass any other parameters to it, since it does not usee them.

.

[haohaoxuexi1]

Thank you, I will try it out

[haohaoxuexi1]

Is there any chance the following code can be included in the function? Or it has to be excluded? @Star Strider

f=-a*subs(fd_d,t,tt)*b/(c)-x*(b/(c))

[Star Strider]

As always, my pleasure!

With respect to your second Comment, it may not have to be excluded, however I would exclude it, since it would just slow everything down and could produce errors. Besides, by definition it calls the Symbolic Math Toolbox, and while that is appropriate in some situations, it is not appropriate here.

As a general rule, it is best to use the Symbolic Math Toolbox for symbolic derivations, and then create numeric functions from them to use in numeric (and especially interative) calculations, and not use the Symbolid Math Toolbox for iterative calculations, such as numerically integrating differential equations.

.

[haohaoxuexi1]

Thank you for your comment.

Yes, I did come into some error while including in the function. You seems have much more experience than I do for matlat coding. If possible, I wish to include it in the function. Would you mind to do some simple try out for me to make it work which may help me quite a bit for my calculation. Anyway, you already help me a lot.

Thanks, @Star Strider

[Star Strider]

As always, my pleasure!

I do not understand what you want to do.

Mixing numeric and symbolic code (as you want to do here) is not adviasable for the reasons I already stated. If the symbolic code has a specific purpose (that is not obvious to me) it might be possible to include it, even though that would create slower and much less efficient code.

The code in your earlier Comment is already included in the existing numeric code to create ‘f’. There is no reason to include it separately in the function, and especially as a Symbolic Math Toolbox call.

.

[haohaoxuexi1]

@Star Strider

Because I am using a Maple Symbolic Math Toolbox, so "matlabFunction" function didn't work with my current matlab, I tested the function in another computer with original matlab, the reason why I used Maple Symbolic Math Toolbox is for faster calculation.

function dx = Output123(tt,x,a,b,c)
    dx = -(b.*x)./c-(a.*b.*(tt.*1.0e+2+tt.^3.*2.4e+2+tt.^8.*6.3e+2))./c;
end

if I could included

-a*subs(fd_d,t,tt)*b/(c)-x*(b/(c))

inside dx equation in the function, I could make it works.

Thanks again.

[Walter Roberson]

Then code it by hand if it is morally important for you.

Reminder: the ode*() functions strictly require that the output is double() or single(), but the output of subs() is always symbolic.

[Star Strider]

@Walter Roberson — Thank you!