In Ode15s, how do I break the time span into smaller intervals and call the solver twice, so that the integration proceeds faster?

Hi, can anyone explain these lines from the Matlab website to me?

and

I understand how splitting the total time span into small intervals can speed up ODE. But in order to implement this method, how exactly do I "call the solver twice"? How to combine the outputs from each call into one? Say my total time span is

tspan=[t0 tf];

and I break it into

tspan1=[t0 t1];
tspan2=[t1 tf];

If I directly call the solver twice like the following,

% Method 1
[ta,y1]=ode15s(@odefun,tspan1,initialCond,solverOptions,additionalParams);
[tb,y2]=ode15s(@odefun,tspan2,initialCond,solverOptions,additionalParams);

I will get two outputs. But all I need is just one, like the [t, y] below.

% Method 2
[t,y]=ode15s(@odefun,tspan,initialCond,solverOptions,additionalParams);

How can I combine the results from method 1 and get only one output? It would be best if there's code or examples. Thank you.

Answer 1

[Torsten]

tspan1=[t0 t1];
[ta,y1]=ode15s(@odefun,tspan1,initialCond,solverOptions,additionalParams);
initialCond=y1(end,:);
tspan2=[t1 tf];
[tb,y2]=ode15s(@odefun,tspan2,initialCond,solverOptions,additionalParams);
t=[ta(1:end-1);tb];
y=[y1(1:end-1,:);y2];

[madhan ravi]

+1 , out of curiosity @Torsten can odextend() be used here?

[Torsten]

I was not aware of this function, but it should be possible to use it in this context.

Thanks for the comment.

[Ziwei Liu]

Thank you!