  The kinetic analyses of many-particle soft matter often employ many
simulation studies of various physical phenomena which supplement the
experimental limitations or compliment the theoretical findings of the study.
Such simulations are generally conducted by the numerical integration
techniques of the governing equations. In the typical case of collisionless
electrostatic systems such as electrostatic plasmas, the Vlasov-Poisson (VP)
equation system governs the dynamical evolution of the particle phase-space.
The one-dimensional position-velocity (1D-1V) particle phase-space, on the
other hand, is known to exhibit direct analogy with ordinary two-dimensional
fluids, wherein the Vlasov equation resembles the fluid continuity equation of
an in-compressible fluid. On the basis of this fluid-analogy, we present, in
this work, a new numerical integration scheme which treats the 1D-1V
phase-space as a two-dimensional fluid vector space. We then perform and
present analyses of numerical accuracy of this scheme and compare its speed and
accuracy with the well-known finite splitting scheme, which is a standardised
technique for the numerical Vlasov-Poisson integration. Finally, we show some
simulation results of the 1D collisionless electrostatic plasma which highlight
the higher speed and accuracy of the new scheme. This work presents a fast and
sufficiently accurate numerical integration technique of the VP system which
can be directly employed in various simulation studies of many particle
systems, including plasmas.
