How can kinetic energy after collision be more than initial kinetic energy in this particular case, where there is no disintegration of matter or something?

A change of frame of reference does not "generate" the extra kinetic energy even though the kinetic energies of each of the particles might change.
There is an illustration of this idea in the answer to Kinetic energy with respect to different reference frames. If one changes the frame of reference the law of conservation of energy is still valid so in every frame of reference there will be the $50\%$ increase in the kinetic energy.

Classically this is a super-elastic collision with the extra kinetic energy coming from the internal energy of the system eg a chemical reaction, a compressed spring releasing its energy etc.

I have written this answer to point out that the increase in kinetic energy has nothing to do with changing the reference frame and answers which hint at this being true are wrong.
Although individual particles might appear to have a different kinetic energy in another reference frame the total kinetic energy of a system under consideration does not change.

In the question there is the following statement which hints that there is “something” which generates kinetic energy.

How can kinetic energy after collision be more than initial kinetic energy in this particular case, where there is no disintegration of matter or something?

A change of frame of reference does not "generate" the extra kinetic energy even though the kinetic energies of each of the particles might change.
There is an illustration of this idea in the answer to Kinetic energy with respect to different reference frames. If one changes the frame of reference the law of conservation of energy is still valid so in every frame of reference there will be the $50\%$ increase in the kinetic energy.

Classically this is a super-elastic collision with the extra kinetic energy coming from the internal energy of the system eg a chemical reaction, a compressed spring releasing its energy etc.

How can kinetic energy after collision be more than initial kinetic energy in this particular case, where there is no disintegration of matter or something?

A change of frame of reference does not "generate" the extra kinetic energy even though the kinetic energies of each of the particles might change.
There is an illustration of this idea in the answer to Kinetic energy with respect to different reference frames. If one changes the frame of reference the law of conservation of energy is still valid so in every frame of reference there will be the $50\%$ increase in the kinetic energy.

Classically this is a super-elastic collision with the extra kinetic energy coming from the internal energy of the system eg a chemical reaction, a compressed spring releasing its energy etc.

In the centre of mass frame of reference moving at speed $\frac {v_{\rm o}}{2}$, the magnitude of the initial momentum of each of the particles is $m\left (\frac{v_{\rm o}}{2}\right )$ with each having a final momentum of $m v_{\rm f}$.

Equating energies $\frac12 m v^2_{\rm f}+ \frac12 m v^2_{\rm f} +\frac12 (2m) \left (\frac {v_{\rm o}}{2} \right )^2 = \frac 12 m v^2_{\rm o} + \frac 12 \left (\frac 12 m v^2_{\rm o}\right )$ enables one to find the required relative velocity, $2v_{\rm f}$.

How can kinetic energy after collision be more than initial kinetic energy in this particular case, where there is no disintegration of matter or something?

A change of frame of reference does not "generate" the extra kinetic energy even though the kinetic energies of each of the particles might change.
There is an illustration of this idea in the answer to Kinetic energy with respect to different reference frames. If one changes the frame of reference the law of conservation of energy is still valid so in every frame of reference there will be the $50\%$ increase in the kinetic energy.

Classically this is a super-elastic collision with the extra kinetic energy coming from the internal energy of the system eg a chemical reaction, a compressed spring releasing its energy etc.