# High order approximation for the Boltzmann equation without angular cutoff

## TL;DR

This paper introduces a new model to approximate the Boltzmann equation without angular cutoff, combining the Boltzmann and Landau operators, and demonstrates higher accuracy and well-posedness.

## Contribution

It proposes a novel approximation model that integrates Boltzmann and Landau operators, achieving higher order accuracy without angular cutoff.

## Key findings

- Proved well-posedness of the approximate equation
- Established error estimates between approximate and original solutions
- Achieved higher order accuracy compared to standard methods

## Abstract

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.