IMPLICIT CONSERVATIVE MONOTONE SCHEMES OF HIGHER ACCURACY FOR NUMERITCALY SOLVING THE TRANSPORT EQUATION
O. S. Sokolov VANT. Ser. Mat. Mod. Fiz. Proc 1998. Вып.1. С. 3140.
For solving numerically the transport equation, one of the approaches is propped to construct implicit conservative monotone difference schemes of higher accuracy with nonlinear correction of the solution based on DS_{n}method. Requirements to the solution are formulated which establish boundaries for output flow variations. It is shown that solution monotonicity and stability follow from these requirement satisfaction. Approximation of the third and fourth orders of accuracy are constructed. The above requirements allow to correct the solution in the case of their violation with an approximation order lowering to the first order under such correction. High accuracy and monotonicity of solutions obtained using the proposed schemes are demonstrated by test problem computation results.
