how with ode45 order we can solve a switching problem?

Hi every one.

I want to write a code like this with ode45. how can I do it?

ode45(func)

func:

mode 1;

if x>=550

mode =2;

if mode=2 and x<=510

mode=1;

x'=f(x)= 0.1*x-50 mode =1

0.1*x-56 mode=2

I write this code, but gives me not correct output in figure

clc;
clear all;
close all;
deltat=10^-2;
x1(1)=510;
x11(1)=550;
for i=1:1000
    x1(i+1)=(0.1*x1(i)-50)*deltat+x1(i);
    y1(i)=x1(i);
    
    if x1(i+1)>=550 && x1(i+1)==(0.1*x1(i)-50)*deltat+x1(i)  
        %return i;
        x1(i+1)=(0.1*x1(i)-56)*deltat+x1(i);
       y1(i)=x1(i);
    elseif x1(i+1)<=510 && x1(i+1)==(0.1*x1(i)-56)*deltat+x1(i)
          %return i;
            x1(i+1)=(0.1*x1(i)-50)*deltat+x1(i);
            y1(i)=x1(i);  
      end
    end
       figure(1)
       plot(i,y1(i))

And what may I do to ruturn "i" as index when "x" reaches 550 or 510?

writing the above code "return i" it gives this error:

Error: File: ntest.m Line: 12 Column: 16

Invalid expression. Check for missing multiplication operator, missing or unbalanced delimiters, or other syntax

error. To construct matrices, use brackets instead of parentheses.

Thanks

Answer 1

[Stephan]

https://de.mathworks.com/help/matlab/math/ode-event-location.html

[azam ghamari]

I go ahead and chenge my program to this:

function dx = rigid(t,x)
   dx=zeros(1,1);
   dx=0.1*x-50;

   if dx==0.1*x-50 && x>=550
        dx=0.1*x-56;
   elseif dx==0.1*x-56 && x<=510
       dx=0.1*x-50;
     end
   if dx==0.1*x-50 && x>=550
         dx=0.1*x-56;
   end
   
     for rigid function and for calling it in another mfile I write this code:
                 
   
  Close all;
clc;
[T,X] = ode45(@rigid,[0,100],[510]);
%        figure(1)
% dxxxx = rigid([0,100],[510])
plot(T,X)      
   

but it does not give me the right answer. I expect that it gives me a curve between 510 , 550 . but it gives me a curve starting from 510 and goaes up to 1700, it does not switch between these 2 functions (dx=0.1x-50 , dx-0.1x-56)why?

[Stephan]

Did you read the informations from the suggested link carefully? The event function is an extra function, so that you dont need a control structure to achieve a switching behaviour during the integration

[azam ghamari]

Hi, Two days ago I answered you, that I actually read it and I don't know how shall I use the odeXY. please see my answer in below.

and may you please write that code (that I wrote with ode45) with ODEXY?

Thanks and Best Reagards.

[Stephan]

At the moment im on vacation and have no access to my computer.

Answer 2

[azam ghamari]

I see it , but I am not sure to undrestand some parts for example:

isterminal(i) = 1 if the integration is to terminate when the ith event occurs. Otherwise, it is 0.

what does it mean exactly?

and I write the code without ode:

clc;
clear all;
close all;
deltat=1;
x1(1)=510;
x11(1)=550;
x1(2)=(0.1*x1(1)-50)*deltat+x1(1);
for i=1:1000
    y1(i)=x1(i);
    
    if (x1(i+1)>=550 && x1(i+1)==(0.1*x1(i)-50)*deltat+x1(i))||(x1(i+1)<=550 && x1(i+1)==(0.1*x1(i)-56)*deltat+x1(i))  
        %return i;
        x1(i+2)=(0.1*x1(i+1)-56)*deltat+x1(i+1);
       y1(i)=x1(i);
    elseif (x1(i+1)<=510 && x1(i+1)==(0.1*x1(i)-56)*deltat+x1(i))||(x1(i+1)>=510 && x1(i+1)==(0.1*x1(i)-50)*deltat+x1(i))
          %return i;
            x1(i+2)=(0.1*x1(i+1)-50)*deltat+x1(i+1);
            y1(i)=x1(i);  
      end
    end
       figure(1)
       plot(x1)

Iand it gives me the result, and I want to write teh code with ode function , how can I change my before code taht I sent befor (with ode) based on this code in away that I get the result ?(with odeXY that you introduced)

Thanks