adding noise to the solution obtained from ode45/dde23

what is the best way to add noise to the solution obtained from the solver like ode45/dde23?

Answer 1

[Sam Chak]

Hi @Muhammad,

Does it work if you execute the following?

[t, y] = ode45(@odefun, tspan, y0);
noise  = mynoise(t);    % user-defined math function for noise
ynoise = y + noise;     % additive method

[Muhammad]

is your approach/method remain same, if we obtain a sol like this: sol = ode45(@odefun,tspan,y0)?

[Sam Chak]

Hi @Muhammad

In theory, the approach remains the same. You store the ode45 solution in sol as a structure array, and then you need to evaluate the structure at n points in the interval to obtain the data y.

%% ODE
odefun = @(t, y) [y(2); - y(1) - 2*y(2)];
tspan  = [0 10];
y0     = [1; 0];

%% Direct Method 
[t, y] = ode45(odefun, tspan, y0);
whos t y 

  Name       Size            Bytes  Class     Attributes

  t         73x1               584  double              
  y         73x2              1168  double              

%% 'sol' Method 
sol    = ode45(odefun, tspan, y0);
t      = linspace(0, 10, 73)';
y      = deval(sol, t)';
whos t y sol

  Name       Size            Bytes  Class     Attributes

  sol        1x1              5178  struct              
  t         73x1               584  double              
  y         73x2              1168  double              

[Muhammad]

Thank you for your help

Answer 2

[Jalal Khan]

The best way to add noise to the solution obtained from solvers like ode45 or dde23 depends on the specific requirements of your problem and the characteristics of the noise you want to introduce

[Muhammad]

like if we are dealing with differential equations for ODE case lorenz equation and DDE mackey glass equation