How to conditionally solve two ODEs simultaneously using 'if-else' ?

Hello there,

I'm modeling acceleration performance of an electric vehicle (i.e velocity vs time plot).

I have two conditions:

1. For velocity less than 39.9 m/s, the velocity will be calculated by this ODE: dv/dt= 9.513-(0.00032*v^2)

2. For velocity greater than or equal to 39.9 m/s, the velocity will be calculated by this ODE: dv/dt= 13.43-(0.922*v)-(0.00032*v^2).

The solution of these ODEs should give me a plot of velocity Vs. time. I tried ode45 & if-else loop for this code, but the code only solves 1st ODE and directly jumps to plotting the results without solving for the 2nd condition. Hence I'm getting a top speed of 615km/h, which is not a correct value.

I request, please guide me through this problem.

Thank you.

    clc; clear all;
    tspan = linspace(0,50,501);  %time in s
    v=0;
    if v<39.9  %velocity in m/s
    [t,v] = ode45(@(t,v) 9.513-(0.00032*v.^2), tspan, v);
    elseif v>=39.9
    [t,v] = ode45(@(t,v) 13.43-(0.922*v)-(0.00032*v.^2), tspan, v);
    end
    kph=v*3.6;  %converting m/s to km/h
    plot(t,kph)
    xlabel('time S')
    ylabel('speed kph')

Answer 1

[Aquatris]

ode45 does not check its values between start and end time. That is why you need to write your own solver or include the ifelse inside your function. I wrote the latter below.

 function vd = fun1(t,v)
    if v <39.9
      vd = 9.513-(0.00032*v.^2);
    elseif  v >= 39.9
      vd = 13.43-(0.922*v)-(0.00032*v.^2);
    end 
  end

Then in the main script, you call

   tspan = linspace(0,50,501);  %time in s
   v=0;
   [t,v] = ode45(@fun1, tspan, v);

[Sagar Dhuri]

Dear Aquatris,

Thanks you very much for your help. i really appreciate it.

This code sorted out the issue completely.