NUMERICAL SOLUTIONS TO THE CAUCHY PROBLEM FOR THE GENERALIZED NON-ISOTROPIC DIFFUSION EQUATION
;
Diffusion, Monte Carlo method, approximate solutions, unbiased estimates, algorithm, algorithm efficiency.Abstrak
This article discusses one of the modern methods (Monte Carlo method) for solving boundary value problems for an ultraparabolic equation of mathematical physics. Based on the obtained results, some numerical estimates of the solution to the Cauchy type problem were carried out.
Iqtiboslar
S.M. Ermakov, A.S. Rasulov, M.T. Bakoev, A.Z. Vaselovskaya. Selected algorithms of the Monte Carlo method / Tashkent: University, 1992. 132 p.
M.Bakoev Solution of a mixed problem for the Kolmogorov equation. // Problems of computational and applied mathematics, No. 2 2019, pp. 60-70. (01.00.00., No. 9)
Doob J.L. Classical Potential Theory and its. Probabilistic Counterpart. Springer-Varlag. 1984. 846 p.
Kolmogorov A.N. Is ber die analitichen Metho der in der Wahrscheinlichkeizsrechnung. Mathemat. Annalen. 1931. 104 p. 415-458.
T.T Halimovich, I.S Mamirovich. Monte Carlo method for constructing an unbelised assessment of diffusion problems. European science review, 2020
Tozhiev T.Kh., Ibragimov Sh.M. Stochastic approximation methods for solving diffusion problems. “Fundamental and applied scientific research: current issues, achievements and innovations” collection of articles of the XVI International Scientific and Practical Conference. – Penza: ICNS “Science and Enlightenment”. – 2018, 13-15 p.
Tozhiev T, Abdullaev SH, Creation of new numerical simulation algorithms for solving initial-boundary-value problems for diffusion equations - AIP Conference Proceedings, 2023
Тожиев.Т-Применение методов монте-карло для аппроксимации диффузионных задач.international journal of scientific researchers (IJSR) 2024
