MATLAB: Ode45 and sol structure – different results

differential equationsMATLABodeode45solve

I am using ode45 function to get solution of system of equation with this line of code

[zv, pv] = ode45(@fun2, [1 0], [1; 0]);

where Matlab stores my results in pv, and in zv is saved longitudinal coordinate, where pv=f(zv). And usually I got 73 points stored in zv.

On the other side I need to find second derivative of pv, and I use these lines of code:

sol=ode45(@fun2,[1 0],[1; 0]);
[~,SXINT] = deval(sol,sol.x);

With this commands I got the second derivative of pv only in points sol.x and in that case sol.x consist only 19 points. What is the difference, how in zv I got 73 points? Isn't it the same structure? Because in both cases I am looking for steps, where it means longitudinal coordinate for me? Or is sol.x that what I am looking for?

Best Answer

If you look separately at ‘sol.x’, it only has 19 points. If you want to get all the results from your deval call, do this:

[~,SXINT] = deval(sol,zv);

Note that any vector will do in place of ‘zv’ here, providing the values are within the limits of your original tspan vector.

Related Solutions

MATLAB: How to find second derivative as output of ode45

To get the second derivative, the first derivative must be part of the solution "sol".

So you have to solve 8=4*2 equations, namely your original system and new algebraic equations given by

y(5)-dy(1) = 0
y(6)-dy(2) = 0
y(7)-dy(3) = 0
y(8)-dy(4) = 0

This way, "sol" has stored the first-order derivatives of y(1)-y(4) in y(5)-y(8) which can now be differentiated by a call to "deval".

Best wishes

Torsten.

MATLAB: How to add variable to ode45 method

The actual longitudinal coordinate z is transferred to your function "fun" by ODE45:

function f=fun( *z*,p)

You cannot reset this value by

z=0:0.001:1;

and I don't see any reason to do so. Thus just delete the line

z=0:0.001:1;