### APPLICATION OF THE DIFFERENTIAL-DIFFERENCE METHOD FOR SOLVING THE PROBLEMS ABOUT THE CURRENT OF THE INCOMPRESSIBLE LIQUID IN THE RECTANGULAR AREA AT THE SMALL NUMBERS OF THE REINOLDS

Jamol Ismatullayevich Khujaev, Scientific And Innovation Center Of Information And Communication Technologies
2018 Theoretical & Applied Science
Impact Factor: ISRA (India) = 1.344 ISI (Dubai, UAE) = 0.829 GIF (Australia) = 0.564 JIF = 1.500 SIS (USA) = 0.912 РИНЦ (Russia) = 0.156 ESJI (KZ) = 4.102 SJIF (Morocco) = 5.667 ICV (Poland) = 6.630 PIF (India) = 1.940 IBI (India) = 4.260 Philadelphia, USA 37 QR -Issue QR -Article Abstract: In this paper, we propose a method of applying the method of lines, which has been developed in detail for the Dirichlet problem, in solving two-dimensional problems of hydrodynamics. The advantage of the
more » ... hod is to exclude the input of fictitious time in solving the equations of the current and pressure function, since finite-difference equations with respect to two Cartesian coordinates are solved simultaneously and accurately. The structure of the main tridiagonal matrices of the transition to finite difference equations remains the same for the case of using separate equations of the stream function, vorticity, and pressure. For the exact solution of finitedifference equations, the eigenvalues and vectors of the basic transition matrix are attracted, the values of the elements of which are calculated only once. Аннотация: В работе предлагается способ применения метода прямых, который подробно разработан для задачи Дирихле, при решении двухмерных задач гидродинамики. Преимущество метода заключается в исключении ввода фиктивного времени при решении уравнений функции тока и давления, так как конечноразностные уравнения по двум декартовым координатам решаются одновременно и точно. Структура основных трехдиагональных матриц перехода к конечноразностным уравнениям остается одинаковой для случая использования отдельных уравнений функции тока, завихренности и