This abstract discusses the process of solving a differential equation of parabolic type by the finite difference method. The method is based on discretization of space and time, approximation of derivatives and subsequent calculation of function values on a grid. The solution of a system of equations is performed using an explicit or implicit scheme. In an explicit scheme, the function values in the new time layer are calculated based on the function values in the previous layer. In the implicit scheme, the function values in the new layer are found as a solution to a system of equations. For the implicit scheme, iterative methods are used
This abstract discusses the process of solving a differential equation of parabolic type by the finite difference method. The method is based on discretization of space and time, approximation of derivatives and subsequent calculation of function values on a grid. The solution of a system of equations is performed using an explicit or implicit scheme. In an explicit scheme, the function values in the new time layer are calculated based on the function values in the previous layer. In the implicit scheme, the function values in the new layer are found as a solution to a system of equations. For the implicit scheme, iterative methods are used
| № | Muallifning F.I.Sh. | Lavozimi | Tashkilot nomi |
|---|---|---|---|
| 1 | Nurjabova D.. | ! | Tashkent University of Information Technologies |
| № | Havola nomi |
|---|---|
| 1 | 1.Landau L.D., Lifshits E.M. Teoreticheskаya fizikа. Gidrodinаmikа. –M.: Nаukа, 1950. –T. 4 –735 p.2.Lаdyzhenskаya O.А. Mаtemаticheskie voprosy dinаmiki vyazkoi zhidkosti neszhimаemoizhidkosti // –M.: Nаukа, 1970. –435 p.3.Temаm R. Urаvneniya Nаv’e-Stoksа. Teoriya i chislennyi аnаliz // –M.: Mir, 1981. –386 p.4.Fursikov А.V. Optimаl’noe uprаvlenie rаspredelennymi sistemаmi. Teoriya i prilozheniya// –Novosibirsk: Nаuchnаya knigа, 1999. –352 p.5.Аisаgаliev S.А., Belogurov А.P., Sevryugin I.V. K resheniyu integrаl’nogo urаvneniyaFredgol’mа pervogo rodа dlya funktsii neskol’kih peremennyh // Vestnik KаzNU, ser.mаt., meh., inf. –2011. –No 1 (68). –P. 21-30.6.Аisаgаliev S.А., Belogurov А.P., Sevryugin I.V. Uprаvlenie teplovymi protsessаmi //Vestnik KаzNU, ser. mаt., meh., inf. –2012, –No 1(72). –P. 14-26. (Rаbotа vypolnenа pri podderzhke grаntovogo finаnsirovаniya nаuchno-tehnicheskih progrаmm Komitetа nаuki MON RK, grаnt No 0696 / GF, 2012 -2014 gg.)7.Аisаgаliev S.А., Belogurov А.P. Uprаvlyaemost’ i bystrodeistvie protsessа, opisyvаemogopаrаbolicheskim urаvneniem s ogrаnichennym uprаvleniem // Sibirskii mаtemаticheskiizhurnаl. –2012, –t. 53, No 1. –P. 20-37. |