Maqolada giperbolik tipdagi xususiy hosilali differensial tenglamalar sistemasining (giperbolik sistemalarning) sonli
yechimlarini topish uchun zamonaviy hisoblash metodlari quriladi va tadqiq etiladi. Giperbolik tenglamalar sistemasi
fizikaning turli sohalarida, akustika, gaz dinamikasi, elastiklik nazariyasi, magnit gidrodinamikasi, mayda suv
tenglamalari va boshqa sohalarda uchraydi. Turli sonli metodlarni yagona yondashuv orqali tadqiq etish maqsadida
maqolada bir o`lchovli va ko`p o`lchovli xususiy hosilali chiziqli va chiziqsiz giperbolik tenglamalar yechishda
qo`llaniladigan ishonchli zamonaviy hisoblash metodlarini yaratishga harakat qilingan. Godunov, Laks, Rusanov va
yangi oshkor ayirmali sxemalarning turg`unligi tadqiq etilgan. Maqoladagi natijalar dastlabki differensial masala
yechimining mavjud va yagonaligini ta`minlaydi.
The article describes and examines modern numerical methods for the numerical solution of partial differential
equations of hyperbolic systems (shortly hyperbolic system). Hyperbolic equations can be found in many areas of
physics and mechanics, such as acoustics, fluid dynamics, elasticity theory, magneto-hydrodynamics, shallow water
equations, and others. The article is designed for researchers who are faced with the necessity of solving hyperbolic
systems in various areas of mechanics, physics and applied mathematics. The feature of the article is to present and
classify the different numerical methods expounded on the basis of a single common approach. The article aims to
provide a set of reliable modern numerical methods to solve linear and nonlinear hyperbolic systems of partial
differential equations in one-dimensional and multidimensional cases. Some well-known difference schemes such as
Godunov, Lax and Rusanov are discussed, and new explicit finite difference schemes are suggested.
Рассматриваются современные численные методы решения уравнений в частных производных
гиперболических систем. Гиперболические системы встречаются во многих областях физики и механики, такие
как акустика, гидродинамика, теория упругости, магнитная гидродинамика, уравнения мелкой воды и др.
Статья предназначена для исследователей, которые сталкиваются с необходимостью решения гиперболических
систем в различных областях механики, физики и прикладной математики. Особенностью работы является
представление и классификация различных численных методов (явные разностные схемы), изложенных на
основе единого общего подхода. Также исследуется вопрос устойчивости некоторых известных разностных
схем, таких как схема Годунова, Лакса и Русанова , а также новые явные разностные схемы.
Maqolada giperbolik tipdagi xususiy hosilali differensial tenglamalar sistemasining (giperbolik sistemalarning) sonli
yechimlarini topish uchun zamonaviy hisoblash metodlari quriladi va tadqiq etiladi. Giperbolik tenglamalar sistemasi
fizikaning turli sohalarida, akustika, gaz dinamikasi, elastiklik nazariyasi, magnit gidrodinamikasi, mayda suv
tenglamalari va boshqa sohalarda uchraydi. Turli sonli metodlarni yagona yondashuv orqali tadqiq etish maqsadida
maqolada bir o`lchovli va ko`p o`lchovli xususiy hosilali chiziqli va chiziqsiz giperbolik tenglamalar yechishda
qo`llaniladigan ishonchli zamonaviy hisoblash metodlarini yaratishga harakat qilingan. Godunov, Laks, Rusanov va
yangi oshkor ayirmali sxemalarning turg`unligi tadqiq etilgan. Maqoladagi natijalar dastlabki differensial masala
yechimining mavjud va yagonaligini ta`minlaydi.
| № | Имя автора | Должность | Наименование организации |
|---|---|---|---|
| 1 | Aloyev R.D. | professor | Mirzo Ulug'bek nomidagi O'zbekiston Milliy universiteti |
| 2 | Xudoyberganov M.U. | dotsent | Mirzo Ulug'bek nomidagi O'zbekiston Milliy universiteti |
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