Solving a system of ODEs with conditionally defined coefficient

Hi, I want to plot on the interval the solution of the following system of ODEs

with the initial conditions

,

where

.

I wrote the function, by defining the coefficient f, using "piecewise" sintax:

    function dzdt=odefunw1(t,z)
    syms t
    f=piecewise(0<=t<1, -2*t^2+3*t, t>=1, 1/t);
    dzdt=zeros(2,1);
    dzdt(1)=z(2);
    dzdt(2)=z(1)-f*z(2);
    end

In the Command Window, I wrote

    tspan = [0 1000];
    z0 = [0.1 0.1];
    [t,z] = ode45(@(t,z) odefunw1(t,z), tspan, z0);
    plot(t,z(:,1),'g',t,z(:,2),'b')

But several errors occured. Where do I wrong and how could I fix it? Thanks in advance.

Answer 1

[darova]

replace

 f=piecewise(0<=t<1, -2*t^2+3*t, t>=1, 1/t); 

with

if t >= 1
    f = 1/t;
else
    f = -2*t^2+3*t;
end

[Cris19]

Thank you for the answer, but it's not working.

I wrote the function

   function dzdt=odefunw1(t,z)
    syms t
    if t >= 1
     f = 1/t;
    else
     f = -2*t^2+3*t;
    end;
    dzdt=zeros(2,1);
    dzdt(1)=z(2);
    dzdt(2)=z(1)-f*z(2);
    end

and the commands

tspan = [0 100];
z0 = [0.1 0.1];
[t,z] = ode45(@(t,z) odefunw1(t,z), tspan, z0);
plot(t,z(:,1),'r',t,z(:,2),'b')

and the following errors occured:

Conversion to logical from sym is not possible.

Error in odefunw1 (line 3)
    if t >= 1

Error in @(t,z)odefunw1(t,z)

Error in odearguments (line 90)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

Error in ode45 (line 115)
    odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin)

[darova]

You are overwriting t variable. Remove this line:

syms t

[Cris19]

It worked! Thank you very much!