  Motivated by developments in string theory, such as T-duality, it has been
proposed that the geometry of spacetime should have an intrinsic minimal length
associated with it. This would modify the short distance behavior of quantum
systems studied on such a geometry, and an optical analog for such a short
distance modification of quantum system has also been realized by using
non-paraxial nonlinear optics. As general relativity can be viewed as an
effective field theory obtained from string, it is expected that this would
also modify the short distance behavior of general relativity. Now the
Newtonian approximation is a valid short distance approximation to general
relativity, and Schrodinger-Newton equation can be obtained as a
non-relativistic semi-classical limit of such a theory, we will analyze the
short distance modification of Schrodinger-Newton equation from an intrinsic
minimal length in the geometry of spacetime. As an optical analog of the
Schrodinger-Newton equation has been constructed, it is possible to optically
realize this system. So, this system is important, and we will numerical
analyze the solutions for this system. It will be observed that the usual
Runge-Kutta method cannot be used to analyze this system. However, we will use
a propose and use a new numerical method, which we will call as the two step
Runge-Kutta method, for analyzing this system.
