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The BEC is described by the Gross Pitaevskii equation, which can be solved numerically using the Crank Nicholson method.
The model equations cannot be solved analytically, since the domain contains a moving interface, and must therefore be solved numerically, using specific methods designed for that purpose.
These equation will later be solved numerically using the software package COMSOL Multiphysics [27].
(42) and (41) can be solved numerically using the definitions in (5).
Problem (16) can be solved numerically using Monte Carlo simulation for a given P ( N, L ).
The nonlinear Boussinesq equation can be solved numerically using the Mac Cormack scheme of explicit finite difference method (Bansal [2013]).
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The equilibrium equations are solved numerically using Mathematica.
The model was solved numerically using the finite difference method.
Governing equations are solved numerically using implicit methods.
The transformed boundary layer equations are solved numerically using MATLAB (bvp4c).
The time dependent form of Reynolds equation is solved numerically using the finite-difference method.
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