how I can fix sample time in ode45

I want to fix the sample time (for example, T=0.5) in ode45. How can I do it? If it is not possible, do we have another way to fix the sample time in Matlab?

tspan = 0:1:10000;
y0 = [0.2,0.3];
[t,y] = ode45(@(t,y) odefcn(t,y), tspan, y0);
% 

function dx = odefcn(t,x)
dx = zeros(2,1);
u=[2 -2]*x(1:2)+1;
dx(1)=x(1)-2*x(2)
dx(2)=-x(2)+u
end

Answer 1

[Sam Chak]

Hi @hossen hassanzadth

Are you looking for something like this?

T      =  0.5;
tspan  =  0:T:10;
y0     = [0.2,0.3];
[t, y] = ode45(@(t,y) odefcn(t,y), tspan, y0);
plot(t, y, '-o'), grid on
xlabel('Time')

% 
function dx = odefcn(t,x)
    dx    = zeros(2,1);
    u     = [2 -2]*x(1:2) + 1;
    dx(1) =   x(1) - 2*x(2);
    dx(2) = - x(2) + u;
end

[hossen hassanzadth]

Hi, thank you. I tried your method, but this method did not fix the sample time. When I debug it, see ode45 solve it with variable sample time.

[Sam Chak]

Indeed, ode45() solver employs its own internal steps for computing the solution and subsequently assesses the solution at the designated points in tspan. Nonetheless, it is crucial to emphasize that the solutions generated at the specified points exhibit the same level of accuracy as the solutions computed at each internal step. Another approach is to use deval().

tspan  = [0, 10];
y0     = [0.2, 0.3];
sol    = ode45(@(t,y) odefcn(t,y), tspan, y0);

T      = 0.5;
t      = 0:T:10;
y      = deval(sol, t);
plot(t, y, '-o'), grid on
xlabel('Time')

function dx = odefcn(t,x)
    dx    = zeros(2,1);
    u     = [2 -2]*x(1:2) + 1;
    dx(1) =   x(1) - 2*x(2);
    dx(2) = - x(2) + u;
end

[Sam Chak]

Hi @hossen hassanzadth

Else everything fails, you can write a simple algorithm using the convetional Runge–Kutta solver that allows the fixed step size for the integration..

h      = 0.5;
x      = 0:h:10;

% Initial values
y(:,1) = [0.2 0.3];

% Input signal
u      = @(y) [2 -2]*y + 1;

% State equations
odefcn = @(t, y) [y(1) - 2*y(2);
                - y(2) + u(y)];

% Runge-Kutta ODE Solver
for i = 1:(length(x)-1)
    k1     = odefcn(x(i),       y(:,i));
    k2     = odefcn(x(i)+0.5*h, y(:,i)+0.5*h*k1);
    k3     = odefcn(x(i)+0.5*h, y(:,i)+0.5*h*k2);
    k4     = odefcn(x(i)+h,     y(:,i)+k3*h);
    y(:,i+1) = y(:,i) + (h/6)*(k1 + 2*k2 + 2*k3 + k4);
end

plot(x, y, '-o'), grid on
xlabel('Time')

Answer 2

[Walter Roberson]

You cannot do that. ode45() is always a variable-step solver. So is ode15s, ode23s, ode78, ode113, ode89.

If you need a fixed step solver then see https://www.mathworks.com/matlabcentral/answers/98293-is-there-a-fixed-step-ordinary-differential-equation-ode-solver-in-matlab-8-0-r2012b#answer_107643