how I can fix sample time in ode45
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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
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採用された回答
Sam Chak
2023 年 10 月 29 日
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
3 件のコメント
Sam Chak
2023 年 10 月 29 日
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
2023 年 10 月 29 日
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')
その他の回答 (1 件)
Walter Roberson
2023 年 10 月 29 日
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
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