ode4 in simulink and Fourth-order Runge-kutta (RK4) formula

Do the results of using simulink ode4 solver to solving differential equations and using matlab RK4 to solving the same differential equation are same? I set the same time step and the initial value. Why did I get different results, there are some error between the two results.

[SePl]

Same here, and so far i did not find a solution in the last days! Tried the same for ode1 and implemented the euler method and for that the error between those two is almost zero! Also for Heun the error is almost exactly the same as for Runge-Kutta. See my code for RK4 below, but i did just as said in the mathworks tutorial and just changed the names of the variables.

 function [xout] = ode4(F,t0,h,tf,x0);
   x = x0;
   xout = x'; 
    for t = t0 : h : tf-h;

        s1 = F(t, x);
        s2 = F(t+h/2, x+h*s1/2);
        s3 = F(t+h/2, x+h*s2/2);
        s4 = F(t+h, x+h*s3);

        x = x + h*(s1 + 2*s2 + 2*s3 + s4)/6;

        xout = [xout; x'];

    end
 end

Help would be great! Need that for a realtime simulation and euler is just not exact enough!!

[manmai]

I also have a question about how Simulink runs ode4. It runs this solver in the same manner as Matlab or in the other way. As we know, when we integrate the ODE with the Fourth-order Runge-kutta method we call the differential equations (function), named fx(), 4 times. But when i run a simulink model with ode4, simulink executes model only 1 time, instead of 4. My simple model is shown in attached figure. The output of MatlabFunction increases by 1 after every execution. Fix-step is chosen and equal 0.1s. Integration time is 0.1s. Output of block MatlabFunction is 1, while in Matlab code, realizing the same model, i've got 4. So my question is, if Simulink really executes model only one time, instead of 4 times, on every step of ode4, in what meaning Simulink realizes the runge-kutta 4 method? When using ode4, every time the function fx() is called, the inputs and ouputs may change their values (for example, when we integrate the equations of airplane motion, every time these equations are called we have got the different values of airplane state, of aerodynamic coefficients, of enviroment parameters, of engine state and ect). If Simulink executes model only 1 time per integration step, how it can ensure the numerical accuracy? And then what is difference between ode4 and simple first order methods? Thanks!

[Jan]

@manmai: Please do no attach a new question to an existing thread. Open a new thread instead. Thanks.

[manmai]

Im sorry, Jan Simon. I already opened new thread (but, perhaps my post also is the answer to the question above, so please dont delete it, thanks).

[waterhaha]

i'd like to know if you find the reason that why the same model and input for SIMULINK with ode4 solver and VScode with classic RK4 algorithm resulting different result?