ODE45 solver results changes. How to select optimal Reltol and Abstol?

Hi,

I am trying to solve ODE45 for solving an initial value problem. Part of the code is shown here to explain, if required I can attach the full code.

My doubt is, the output from the mentioned state equation seems changing depending on RelTol and Abstol. i.e X. When I was using default, some values are wrong from the required results. Some values are increasing instead of decreasing. Then I have increased tolerance to 1e-6 and 1e-8 , and found the results improving.

How can I decide exactly which tolerance I should change, Reltol or Abstol? Also, how to decide the tolerance value?

options = odeset('RelTol',1e-8,'AbsTol',1e-8);
Tu = linspace(t0,tf,t_segment);

[Tx,X] = ode45(@(t,x) stateEq_s(t,x,u,Tu), Tu, initx, options); % State Equation

% Value of X increases where it should have decreased for tolerances such as 1e-3

% stateEq_S function
function dx = stateEq_s(t,x,u,Tu)
global C Rs Rp Vsmax 

dx = 0; 
load PV_Preq_data.mat;
load PV_3kW_2005_2016M.mat; % Load demand Power
kW = PV_2016M(25200:25200+32400-1);
Preq = Pdc - kW;
Preq = Preq (1:32400);
Preq(1)=0;
u = interp1(Tu,u,t);       % Interploate the control at ode45 time t
Preq = interp1(Tu,Preq,t); % Interpolate the Preq at ode45 time t

for j=1:1:length(Preq)
if Preq(j) > 0
   dx = -1/C*(( 1/(2*Rs)+ 1/Rp )*x(j) - sqrt((x(j)).^2 - 4*Rs*(Preq(j) - u(j))/(Vsmax^2))/(2*Rs));
else if Preq(j) < 0
      dx = -1/C*(( 1/(2*Rs) - 1/Rp )*x(j) - sqrt((x(j)).^2 - 4*Rs*(Preq(j) - u(j))/(Vsmax^2))/(2*Rs));
    else
      dx = -1/C*(( 1/(2*Rs))*x(j) - sqrt((x(j)).^2 - 4*Rs*(Preq(j) - u(j))/(Vsmax^2))/(2*Rs));

    end
    
    end
end

Also, sometimes I get 'NaN' values depending on tolerances.

[darova]

What about stepSize? Did you try to change it?

[Praveen Kumar]

I think you are talking about Tu (generally called as tspan) in my case. If it is, then I have tried two ways,

1. Tu is a tspan as in the code Since all my variables are of step size 1 sec

t0 = 1;tf = 32400;
t_segment = 32400;
Tu = linspace(t0,tf,t_segment);

2.Instead of Tu, I have tried [to tf] also.

[darova]

No, i'm talking about stepsize

options = odeset('RelTol',1e-8,...
                'AbsTol',1e-8,...
                'maxstep',0.01);

Look HERE

[Praveen Kumar]

I will try this. Thanks.

[Ioannis Matthaiou]

Have you found out the source of the problem? I think by having such a switching function may cause instability in the solutions..