Fourth-order Approximation And Numerical Computation For The Basic Equations Of Atmosphere

The basic equations of atmosphere are studied in dynamic meteorology,a fourth-order finite difference schemes and the convergence theorem are provided and proved.Depending on fourth-order approximation for first derivative and second deriva-tive,ghost point values are expanded near boundary and fourth-order interpolation oper-ator,a fourth-order numerical method of solution is proposed.For proving convergence of schemes we construct numerical solutions which are fourth-order consistent with exact solution.The error between constructed and exact solution can be proposed by Schauder estimate for Poisson equation. The error between constructed and numerical solution is fourth-order.