Fourth-order Conservative Linearized Algorithm for Solving Two Dimensional Burgers' Equation

This paper introduces a fourth-order conservative linearized difference scheme for solving two dimensional Burgers' equation. We rigorously prove the conservation of mass and energy of the scheme, as well as its unique existence. Furthermore, we prove that the error in the $H^{1}{}$-norm has second-order temporally and fourth-order spatially. Numerical experiments are conducted to validate the efficiency and precision of the formulated scheme.