MATLAB: Ode45 : order, number of prediction and step time (theory)

ode45

Hi world !

i want to understand the notation in matlab and the ode algorithms.

ODE45 means a classical method of Runge Kutta which an order of 4 for 5 predictions ?

how the step time is chosen by matlab ?

thanks for your answers 🙂

Best Answer

ODE45 is a Runge-Kutta single step solver using the pair of order 4 and 5 solvers as communicated by Dormand and Prince. The parameters for the order 4 and 5 are chosen such, that the a minimum number of function evaluations is required.

The local discretization error is measured by the difference between the order 4 and 5 solutions. The time steps are chosen such, that this difference is smaller than the given relative and absolute tolerances.

You can find all details by reading the code of ODE45, especially the references will be helpful.

Related Solutions

MATLAB: Second Order, Piecewise ODE help

fun=@(t,y)[y(2);-4*y(1)];
y0=[0 0];
tspan=[0 5];
[T1,Y1]=ode45(fun,tspan,y0);
fun=@(t,y)[y(2);-4*y(1)+(t-5)/5;
y0=[Y1(end,1) Y1(end,2)];
tspan=[T1(end) 10];
[T2,Y2]=ode45(fun,tspan,y0);
fun=@(t,y)[y(2);-4*y(1)+1];
y0=[Y2(end,1) Y2(end,2)];
tspan=[T2(end) 20];
[T3,Y3]=ode45(fun,tspan,y0);

Now put T1, T2, T3 and Y1, Y2, Y3 together to get the result of your ODE on [0 20].

Best wishes

Torsten.

MATLAB: Random order, but equally appearance

doc randperm

Best Answer

Related Solutions

MATLAB: Second Order, Piecewise ODE help

MATLAB: Random order, but equally appearance

Related Question