Abstract:
The paper considers the possibilities of the practical application of monotonized difference schemes previously proposed by the author. The author introduced the monotonicity condition for a nonmonotonic scheme. It is shown that monotonized schemes can both completely remove oscillations and reduce the amplitude of oscillations without changing the condition of monotony, besides some properties of monotonized schemes are proved. The author provides examples of monotonizing operators and develops a convenient design for solving time-dependent tasks. The results can be generalized to a wider variety of tasks.
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