Al-Farg'oniy avlodlari (The descendants of Al-Fargani)
Published October 9, 2025 | Version v1
Journal article Open

IKKI PARAMETRLI SINGULYAR QO'ZG'ATILGAN CHEGARAVIY QIYMAT MUAMMOSINI SPEKTRAL-TO'R METODI ORQALI SONLI MODELLASHTIRISH

Authors/Creators

  • 1. f.m.f.d professor, Termiz davlat universiteti, O'zbekiston
  • 2. doktarant, Termiz davlat universiteti, O'zbekiston

Description

Ikki parametrli singuylar qo'zg'atilgan chegaraviy masalaning yechimlari odatda ikkita chegaraviy qatlamlarni o'z ichiga oladi. Ushbu qatlamlarning mavjudligi sababli oddiy sonli usullar bu ko'rinishdagi masalalar uchun samarasiz hisoblanadi. Ushbu maqolada mazkur ko'rinishdagi masalalarni sonli yechish uchun spektral-to'r usuli taklif etiladi. Taklif etilayotgan ishda, spektral-to'r usuli yordamida ikki parametrli singulyar qo'zg'atilgan tenglama uchun differensial masala algebraik masalaga keltirildi. O'tkazilgan sonli hisoblashlar va olingan natijalar boshqa mualliflar natijalari bilan taqqoslandi. Taklif etilyotgan usulning universalligi, yoqori aniqligi, samaradorligi ko'rib chiqilyotgan masalani yechishda ko'rsatildi.

Files

31_887-188-193-Murodov.pdf

Files (394.2 kB)

Name Size Download all
md5:e6b44d8732971353e9fb3526097ade93
394.2 kB Preview Download

Additional details

References

  • J. Bigge, E. Bohl, Deformations of the bifurcation diagram due to discretization, Math. Comput. 45 (172) (1985) 393–403, doi:10.1090/S0025-5718-1985-0804931-X .
  • R.C. DiPrima, Asymptotic methods for an infinitely long slider squeeze-film bearing, J. Lubr. Technol. 90 (1) (1968) 173–183, doi: 10.1115/1.3601534 .
  • K.C. Patidar, A robust fitted operator finite difference method for a two-parameter singular perturbation problem1, J. Differ. Equs. Appl. 14 (12) (2008) 1197 1214, doi: 10.1080/10236190701817383 .
  • M.H. Salih, G.F. Duressa, H.G. Debela, Numerical solution of singularly perturbed self-adjoint boundary value problem using galerkin method, Int. J. Eng. Sci. Technol. 12 (3) (2020) 26–37, doi: 10.4314/ijest.v12i3.3 .
  • A. Kaushik, A. Gupta, An adaptive mesh generation and higher-order difference approximation for the system of singularly perturbed reaction-fiffusion problem, Partial Differential Equations in Applied Mathematics, 2024, https://doi.org/10.1016/j.padiff.2024.100750.
  • P.J. Robinson, M. Indhumathi, M. Manjumari, Numerical solution to singularly perturbed differential equation of reaction-diffusion type in MAGDM problems, in: Applied Mathematics and Scientific Computing: International Conference on Advances in Mathematical Sciences, Vellore, India, December 2017-Volume II, Springer, 2019, pp. 3–12, doi: 10.1007/978-3-030-01123-9_1 .
  • N. Balasubramani, M.G.Prasad, S. Natesan, Fractal quintic spline solutions for singularly perturbed reaction-diffusion boundary-value problems, Applied Numerical Mathematics, 2024, https://doi.org/10.1016/j.apnum.2024.04.015.
  • Yanhua Liu, Yao Cheng, Local discontinuous Galerkin method for a singularly perturbed fourth-order problem of reaction–diffusion type, Journal of Computational and Applied Mathematics, 2024, https://doi.org/10.1016/j.cam.2023.115641.
  • Relja Vulanović, Thái Anh Nhan, An improved Kellogg-Tsan solution decomposition in numerical methods for singularly perturbed convection-diffusion problems, Applied Numerical Mathematics, 2021, https://doi.org/10.1016/j.apnum.2021.07.019.
  • N. Barzehkar, A. Barati, R. Jalilian, Sinc approximation method for solving system of singularly perturbed parabolic convection-diffusion equations, Applied Numerical Mathematics, 2025, https://doi.org/10.1016/j.apnum.2025.05.005.
  • H.G. Debela, G.F. Duressa, Accelerated exponentially fitted operator method for singularly perturbed problems with integral boundary condition, Int. J. Diff. Eqs. 2020 (2020) 1–8, doi: 10.1155/2020/9268181 .
  • G.R. Kusi, A.H. Habte, T.A. Bullo, Layer resolving numerical scheme for singularly perturbed parabolic convection-diffusion problem with an interior layer, MethodsX 10 (2023) 1–7, doi: 10.1016/j.mex.2022.101953 .
  • N. Roy, A. Jha, A parameter uniform method for two-parameter singularly perturbed boundary value problems with discontinuous data, MethodsX (2023) 1–24, doi: 10.1016/j.mex.2023.102004 .
  • M.K. Kadalbajoo, A.S. Yadaw, B-Spline collocation method for a two-parameter singularly perturbed convection–diffusion boundary value problems, Appl. Math. Comput. 201 (1–2) (2008) 504–513, doi: 10.1016/j.amc.2007.12.038 .
  • M.K. Kadalbajoo , A.S. Yadaw , Parameter-uniform ritz-galerkin finite element method for two parameter singularly perturbed boundary value problems, Int. J. Pure Appl. Math. 55 (2) (2009) 287–300 .
  • F.S.Andisso, G.F.Duressa, Graded mesh B-spline collocation method for two parameters singulyarly perturbed boundary value problems, Journal MethodsX.2023. https://doi.org/10.1016/j.mex.2023.102336
  • Bouakkaz,M.,Arar,N.&Meflah,M. Enhanced numerical resolution of the Duffing and Van der Pol equations via the spectral homotopy analysis method employing chebyshev polynomials of the first kind. Journal Applied mathematica and Computitional.2024.https://doi.org/10.1007/s12190-024-02271-5
  • Normurodov Ch.B.,Abduraximov B.F.,Djurayeva N.T. On estimating the rate of convergence of the initial integration method. AIP Conf. Proc. 3244, 020061(2024) https://doi.org/10.1063/5.0242041