That paper has an error in it. The expression

F = ma

is incorrect if the force is in the same direction the body is moving. E.g. if you have a body moving in the +x direction then

$\displaystyle F_x = \gamma^3m_0a_x$

The derivation of this expression is here

Longitudinal and Transverse Mass
What you have in your paper is

$\displaystyle F_x = \gamma m_0a_x$

which is wrong.

I can read more if you'd like but what you've been trying to calculate has already been rigorously been done. See

http://en.wikipedia.org/wiki/Relativistic_rocket
Even if a rocket has constant acceleration in its own frame of reference it will never reach the speed of light. That calculation is also well known. See

http://www.geocities.com/physics_wor...form_accel.htm
Uniform acceleration occurs when a charged particle is placed in a uniform electric field. In the particle's rest frame the force is a constant so the acceleration is uniform. Such a particle can never reach the speed of light.