The Nonlinear Monotonization of Difference Schemes for Linear Advection Equation

The paper is aimed to the construction and testing of four new difference schemes for the numerical solution of one-dimensional linear advection equation, as well as their comparison with the results of known schemes. Two new schemes were obtained on the base of introduction of artificial diffusion with 'limiters'. The analysis has shown that these schemes give a higher accuracy of solution in comparison with other quasimonotonic schemes. Two other schemes were constructed by 'cutting' of solution on the area of solution dependency and conservation of integral balance. Used methods allow to get a new high order accuracy quasimonotonic difference scheme on the base of known schemes without the expansion of scheme pattern.