  Total charge and energy evaluations for the electron beams generated in the
laser wakefield acceleration (LWFA) is the primary step in the determination of
the required target and laser parameters. Particle-in-cell (PIC) simulations is
an efficient numerical tool that can provide such evaluations unless the effect
of numerical dispersion is not diminished. The numerical dispersion, which is
specific for the PIC modeling, affects not only the dephasing lengths in LWFA
but also the total amount of the self-injected electrons. A numerical error of
the order of $10^{-4}-10^{-3}$ in the calculation of the speed of light results
in a significant error in the total injected charge and energy gain of the
accelerated electron bunches. In the standard numerical approach, the numerical
correction of the speed of light either requires infinitely small spatial grid
resolution (which needs large computation platform) or force to compromise with
the numerical accuracy. A simple and easy to implement numerical scheme is
shown to suppress the numerical dispersion of the electromagnetic pulse in PIC
simulations even with a modest spatial resolution, and without any special
treatments to the core structure of the numerical algorithm. Evaluated charges
of the self-injected electron bunches become essentially lower owing to the
better calculations of the wake phase velocity.
