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

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Sagar Dhuri
Sagar Dhuri on 6 Sep 2018
Commented: Sagar Dhuri on 7 Sep 2018
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')

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Accepted Answer

Aquatris
Aquatris on 7 Sep 2018
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);

  1 Comment

Sagar Dhuri
Sagar Dhuri on 7 Sep 2018
Dear Aquatris,
Thanks you very much for your help. i really appreciate it.
This code sorted out the issue completely.

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