Eurasian Journal of Mathematical Theory and Computer Sciences 4-jild 2-son (2024) · 16–24-betlar

HIGH ACCURACY DIFFERENCE SCHEME FOR THE EQUATION OF DYNAMICS OF COMPRESSIVE STRATIFIED ROTATING FLUID

Utebaev, D., Kazimbetova, M.M.

DOI: 10.5281/zenodo.10670608 · Manbada o'qish → · PDF (manba serverida)

Annotatsiya

Difference schemes of the finite difference method of high-order accuracy for the sixth-order Sobolev-type equation are constructed and investigated. In particular, the first boundary value problem for the wave equation of a compressible stratified rotating fluid is considered. First, approximation is performed only in spatial variables by the finite difference method, and the resulting system of high-dimensional ordinary differential equations is also approximated by this method. Using the method of energy inequalities, a priori estimates were obtained and, on their basis, theorems on the stability and convergence of the constructed difference schemes were proven; accuracy estimates were obtained for sufficient smoothness of the solution to the original initial boundary value problem. An algorithm for implementing difference schemes is proposed.

Dynamic equation, stratified fluid, Sobolev-type equation, difference schemes, finite difference method, stability, convergence, accuracy

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