Errors when using the function ODE 45

Hello! Please help me when using ODE 45! I receive errors:

1) Not enough input arguments. Error in peFun (line 5) eta=ALPHA(1);

2) Error in odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

3) Undefined function or variable 'vPUR'

function fval=peFun(t,ALPHA)
tspan=[0 1];

% Get variables

eta=ALPHA(1);
r=ALPHA(2);
beta=ALPHA(3);
alpha=ALPHA(4);
xP=ALPHA(5);
yP=ALPHA(6);
xE=ALPHA(7);
yE=ALPHA(8);

% Constants

vER=3;
vPUR=5;
a=1;

% Describing dALPHA/dt

fval=zeros(8,1);
fval(1,1)=(-vPUR*SIN(beta)+vER*SIN(alpha))/r;
fval(2,1)=vER*COS(alpha)-vPUR*COS(beta);
fval(3,1)=(a/r)*(vER*SIN(alpha)-vPUR*SIN(beta));
fval(4,1)=(-vER*SIN(alpha)+vPER*SIN(beta))/r;
fval(5,1)=vPUR*COS(eta+beta);
fval(6,1)=vPUR*SIN(eta+beta);
fval(7,1)=vER*COS(eta+alpha);
fval(8,1)=vER*SIN(eta+alpha);

% To run P-E system
%%Initialization

eta0=pi/4;
r0=sqrt(2);
beta0=0;
alpha0=pi/4;
xP0=0;
yP0=0;
xE0=1;
yE0=1;

ALPHA0=[eta0;r0;beta0;alpha0;xP0;yP0;xE0;yE0];

%Solve using ODE45

[tSol,ALPHASol]=ode45(@peFun,tspan,ALPHA0);

%Plot the results
plot(tSol,ALPHASol);

Thank you!

Answer 1

[madhan ravi]

tspan=[0 1];
% To run P-E system
%%Initialization
eta0=pi/4;
r0=sqrt(2);
beta0=0;
alpha0=pi/4;
xP0=0;
yP0=0;
xE0=1;
yE0=1;
ALPHA0=[eta0;r0;beta0;alpha0;xP0;yP0;xE0;yE0];
[tSol,ALPHASol]=ode45(@peFun,tspan,ALPHA0);      %function calling before function definition
plot(tSol,ALPHASol);

function fval=peFun(t,ALPHA)

% Get variables
eta=ALPHA(1);
r=ALPHA(2);
beta=ALPHA(3);
alpha=ALPHA(4);
xP=ALPHA(5);
yP=ALPHA(6);
xE=ALPHA(7);
yE=ALPHA(8);
% Constants
vER=3;
vPUR=5;
a=1;
% Describing dALPHA/dt
fval=zeros(8,1);
fval(1,1)=(-vPUR*sin(beta)+vER*sin(alpha))/r;
fval(2,1)=vER*cos(alpha)-vPUR*cos(beta);
fval(3,1)=(a/r)*(vER*sin(alpha)-vPUR*sin(beta));
fval(4,1)=(-vER*sin(alpha)+vER*sin(beta))/r;
fval(5,1)=vPUR*cos(eta+beta);
fval(6,1)=vPUR*sin(eta+beta);
fval(7,1)=vER*cos(eta+alpha);
fval(8,1)=vER*sin(eta+alpha);

end

[Elina Makieva]

I got another problem: >> peFun Not enough input arguments.

Error in peFun (line 3) eta=ALPHA(1);

I will be very grateful if you kindly help me!

[madhan ravi]

I got the graph did you try my answer? see the attached screenshot of the graph in my answer

[Elina Makieva]

Yes, and received such an error...

[Elina Makieva]

This is what I insert

madhan ravi's reply : the second picture in this comment is the file you should run by clicking the green button .

[madhan ravi]

Just copy my answer and save it in a script file and click green button

[Elina Makieva]

Sorry for stupid questions, I`ve just started learning MATLAB. should I insert your answer in two different windows as it was before or how?

[madhan ravi]

just copy my answer from tspan=[0 1]; till end and paste it in command window and press enter

[Elina Makieva]

And again...

[madhan ravi]

paste the code here what you tried ,and delete the two files which you saved before

[Elina Makieva]

tspan=[0 1];
% To run P-E system
%%Initialization
eta0=pi/4;
r0=sqrt(2);
beta0=0;
alpha0=pi/4;
xP0=0;
yP0=0;
xE0=1;
yE0=1;
ALPHA0=[eta0;r0;beta0;alpha0;xP0;yP0;xE0;yE0];
[tSol,ALPHASol]=ode45(@peFun,tspan,ALPHA0);      %function calling before function definition
plot(tSol,ALPHASol);
function fval=peFun(t,ALPHA)
% Get variables
eta=ALPHA(1);
r=ALPHA(2);
beta=ALPHA(3);
alpha=ALPHA(4);
xP=ALPHA(5);
yP=ALPHA(6);
xE=ALPHA(7);
yE=ALPHA(8);
% Constants
vER=3;
vPUR=5;
a=1;
% Describing dALPHA/dt
fval=zeros(8,1);
fval(1,1)=(-vPUR*sin(beta)+vER*sin(alpha))/r;
fval(2,1)=vER*cos(alpha)-vPUR*cos(beta);
fval(3,1)=(a/r)*(vER*sin(alpha)-vPUR*sin(beta));
fval(4,1)=(-vER*sin(alpha)+vER*sin(beta))/r;
fval(5,1)=vPUR*cos(eta+beta);
fval(6,1)=vPUR*sin(eta+beta);
fval(7,1)=vER*cos(eta+alpha);
fval(8,1)=vER*sin(eta+alpha);
end

[Elina Makieva]

oh,sorry

[Elina Makieva]

tspan=[0 1];
% To run P-E system
%%Initialization
eta0=pi/4;
r0=sqrt(2);
beta0=0;
alpha0=pi/4;
xP0=0;
yP0=0;
xE0=1;
yE0=1;
ALPHA0=[eta0;r0;beta0;alpha0;xP0;yP0;xE0;yE0];
[tSol,ALPHASol]=ode45(@peFun,tspan,ALPHA0);      %function calling before function definition
plot(tSol,ALPHASol);
function fval=peFun(t,ALPHA)
% Get variables
eta=ALPHA(1);
r=ALPHA(2);
beta=ALPHA(3);
alpha=ALPHA(4);
xP=ALPHA(5);
yP=ALPHA(6);
xE=ALPHA(7);
yE=ALPHA(8);
% Constants
vER=3;
vPUR=5;
a=1;
% Describing dALPHA/dt
fval=zeros(8,1);
fval(1,1)=(-vPUR*sin(beta)+vER*sin(alpha))/r;
fval(2,1)=vER*cos(alpha)-vPUR*cos(beta);
fval(3,1)=(a/r)*(vER*sin(alpha)-vPUR*sin(beta));
fval(4,1)=(-vER*sin(alpha)+vER*sin(beta))/r;
fval(5,1)=vPUR*cos(eta+beta);
fval(6,1)=vPUR*sin(eta+beta);
fval(7,1)=vER*cos(eta+alpha);
fval(8,1)=vER*sin(eta+alpha);
end

[Elina Makieva]

I can`t insert it in a right formating

madhan ravi's reply: select the whole code and press the code button {} to format your code correctly.

see GIF to understand how it works .

[madhan ravi]

just delete your files peFun.m and runpeFun.m

put clear all at the very beginning and paste the code again in command window and try again

[Elina Makieva]

I just copy your answer and paste in command window and press enter because there is not green button when I work with command window

[madhan ravi]

OMG :) I know but if you press enter you should get the result

[Elina Makieva]

Ok, just a minute

[Elina Makieva]

:))) I deleted all previous files, but... :))

[Elina Makieva]

OMG!!!IT WORKS!!! :)))) THANK YOU A LOT!!!!!! Could you please tell me, why, when I was doing it in two different windows, I received errors? And what was the initial problem, so I would not repeat it again?

madhan ravi's reply: your initial problem was you did everything correctly but you click run button in the function file(it isn't wrong to do that) but in your case it was because your function required inputs that had to be passed to evaluate those equations.

see common errors while calling a function which will make you understand how the function works.

[Elina Makieva]

Could you please tell, what function should I insert to receive global phase portrait like that?

madhan ravi's reply : I don't know what a global phase portrait is, that's why I made this comment

[Bruno Luong]

when I was doing it in two different windows, I received errors?

function should be put in an mfile with right name in an accessible path or in some recent MATLAB release in the bottom of the script Here is the doc

[madhan ravi]

Thank you @Bruno , @Elina just copy my answer and paste in a new script and save it and make sure to accept the answer since it answered your question

[Elina Makieva]

Thank you @Bruno! @Madhan could you please help me with my question about phase portrait? Or I should create new question?

[madhan ravi]

Please create a new question @Elina

[Elina Makieva]

Thank you a lot!

[madhan ravi]

Anytime :)

[Elina Makieva]

I will really appreciate if you could help me with phase portrait https://www.mathworks.com/matlabcentral/answers/429206-errors-when-using-ode-45-phase-portraits