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
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
| № | Имя автора | Должность | Наименование организации |
|---|---|---|---|
| 1 | Utebaev D.. | ! | Karakalpak State University named after Berdakh |
| 2 | Kazimbetova .M. | ! | Karakalpak State University named after Berdakh |
| № | Название ссылки |
|---|---|
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