关键词: nonlinear two-dimensional Newton-Boussinesq equation, classical solution, a priori estimates

Abstract: We discuss the uniformly higher order accurate extrapolations, which are based on the uniform expansion for global error, to solutions of uniformly convergent discretization methods for singularly perturbed problems. By applying the approach to the in-Allen-Southwell scheme for a non-self-adjoint problem, we obtain an extrapolation solution which is uniformly convergent with order two. We confirm the result by numerical calculations.

Key words: nonlinear two-dimensional Newton-Boussinesq equation, classical solution, a priori estimates