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In order to solve the Boltzmann equation numerically, in the present work, wepropose a new model equation to approximate the Boltzmann equation withoutangular cutoff. Here the approximate equation incorporates Boltzmann collisionoperator with angular cut-off and the Landau collision operator. As a firststep, we prove the well-posedness theory for our approximate equation. Then inthe next step we show the error estimate between the solutions to theapproximate equation and the original equation. Compared to the standardangular cut-off approximation method, our method results in higher order ofaccuracy.

High order approximation for the Boltzmann equation without angular cutoff