  In order to solve the Boltzmann equation numerically, in the present work, we
propose a new model equation to approximate the Boltzmann equation without
angular cutoff. Here the approximate equation incorporates Boltzmann collision
operator with angular cut-off and the Landau collision operator. As a first
step, we prove the well-posedness theory for our approximate equation. Then in
the next step we show the error estimate between the solutions to the
approximate equation and the original equation. Compared to the standard
angular cut-off approximation method, our method results in higher order of
accuracy.
