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problem in creating function file using ode45

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I am trying to solve a second order coupled ode using ode45, however I am facing issues in making it function file and providing variables as input. How to convert symbolic input to numerical in main file using ode45.

Accepted Answer

Torsten
Torsten on 11 Mar 2023
Edited: Torsten on 11 Mar 2023
Be careful with the order of the solution vector Y. It is (y, Dy, x, Dx). You have to supply the vector of initial values "ic" in the same order !
rng("default")
clc
clear all
close all
O=rand;
a=rand;
g=9.81;
L=rand;
[y]=coupled_ode(O, a, g, L);
VF = 
Subs = 
ftotal = function_handle with value:
@(t,Y)[Y(2);Y(1).*(-7.725211393067794e+1)-sin(9.057919370756192e-1).*Y(4).*1.629447372786358;Y(4);Y(3).*(-7.725211393067794e+1)+sin(9.057919370756192e-1).*Y(2).*1.629447372786358]
Disp=y;
function [y] = coupled_ode(Onum, anum, gnum, Lnum)
syms O a g L x(t) y(t) t Y
dx = diff(x);
d2x = diff(x,2);
dy = diff(y);
d2y = diff(y,2);
Eq1 = d2x == 2*O*sin(a)*dy - (g/L)*x(t);
Eq2 = d2y == -2*O*sin(a)*dx - (g/L)*y(t);
[VF,Subs] = odeToVectorField(Eq1, Eq2)
VF = subs(VF,[O a g L],[Onum anum gnum Lnum]);
ftotal = matlabFunction(VF,'Vars',{t,Y})
tspan = [0 25]; % Choose Appropriate Simulation Time
ic = [0 1 0 1]; % Choose Appropriate Initial Conditions
[t,y] = ode45(ftotal, tspan, ic);
figure
plot(t, y)
grid
legend(string(Subs))
end
  2 Comments
Susmita Panda
Susmita Panda on 12 Mar 2023
Thank you @ Torsten sir. rng(default) helped me.This is exactly what I was searching.I didnt have any idea about this command.
Torsten
Torsten on 12 Mar 2023
Edited: Torsten on 12 Mar 2023
It's always a good idea if programming parts that serve different tasks have their own subfunctions. But in your case, I don't understand why and how you divided your code in the two different .m files.
E.g. to have control over what is done in the function coupled_ode, you will have to pass tspan, the initial conditions for the variables and the parameter values for O, a, g and L. The values returned should be t and y. The plotting part also should be done in the main program because it makes no sense to do the plotting in coupled_ode while passing the results as output parameters back to the calling program.
I'd arrange the code as
rng("default")
clc
clear all
close all
O = rand;
a = rand;
g = 9.81;
L = rand;
f = function_to_integrate(O, a, g, L)
f = function_handle with value:
@(t,Y)[Y(2);Y(1).*(-7.725211393067794e+1)-sin(9.057919370756192e-1).*Y(4).*1.629447372786358;Y(4);Y(3).*(-7.725211393067794e+1)+sin(9.057919370756192e-1).*Y(2).*1.629447372786358]
tstart = 0.0;
tend = 25.0;
tspan = linspace(tstart,tend,100); % Choose Appropriate Simulation Time
ic = [0 1 0 1]; % Choose Appropriate Initial Conditions
[t,y] = ode45(f, tspan, ic);
figure
plot(t, y)
grid
legend(string(Subs))
Unrecognized function or variable 'Subs'.
function f = function_to_integrate(Onum, anum, gnum, Lnum)
syms O a g L x(t) y(t) t Y
dx = diff(x);
d2x = diff(x,2);
dy = diff(y);
d2y = diff(y,2);
Eq1 = d2x == 2*O*sin(a)*dy - (g/L)*x(t);
Eq2 = d2y == -2*O*sin(a)*dx - (g/L)*y(t);
[VF,Subs] = odeToVectorField(Eq1, Eq2);
VF = subs(VF,[O a g L],[Onum anum gnum Lnum]);
f = matlabFunction(VF,'Vars',{t,Y});
end

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More Answers (1)

Alan Stevens
Alan Stevens on 10 Mar 2023
Are you looking for something like this? (I might have misinterpreted your equations!)
O=1;
a=pi/2;
g=9.81;
L=100;
tspan = [0 15]; % Choose Appropriate Simulation Time
ic = [0 1 0 1]; % Choose Appropriate Initial Conditions
[t,y] = ode45(@(t,y) ftotal(t,y,O,a,g,L), tspan, ic);
figure
plot(t, y)
grid
legend('y1','dy1/dt','y2','dy2/dt')
function dydt=ftotal(~,y,O, a, g, L)
y1 = y(1); v1 = y(2); y2 = y(3); v2 = y(4);
dydt = [ v1;
2*O*sin(a)*y2 - g/L;
v2;
-2*O*sin(a) - g/L*y1];
end
  6 Comments
Susmita Panda
Susmita Panda on 11 Mar 2023
Thank you @Torsten sir for this method. I will try this.
but is there any way we can call function "coupled_ode" in "Main_file" which I posted without error. This method is convenient to me and produces good result when they variables are called in same file.I am getting error of this kind when I am making it function file and providing variables in "Main_file":
Error using superiorfloat
Inputs must be floats, namely single or double.
Error in odearguments (line 114)
dataType = superiorfloat(t0,y0,f0);
Error in ode45 (line 107)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);
Error in coupled_ode (line 18)
[t,y] = ode45(@(t,y) ftotal(t,y,O,a,g,L), tspan, ic);
Error in Main_file (line 9)
[y]=coupled_ode(O, a, g, L);
Walter Roberson
Walter Roberson on 12 Mar 2023
After you get the xddot and yddot using solve(), call odeFunction to create something to pass to ode45() .
I recommend following the workflow shown in the first example to odeFunction

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