NUMERICAL MODELING OF NONLINEAR PARABOLIC TYPE DIFFERENTIAL EQUATION
Abstract
In this article, the boundary value problem posed for a one-dimensional quasilinear heat transfer equation of a nonlinear parabolic type is numerically modeled using an explicit separation scheme. The heat transfer coefficient is taken as proportional to temperature: k(u) u The initial temperature distribution is parabolic, and the temperature at the boundaries is assumed to be zero. The stability condition of the separation scheme obtained as a result of discretization is determined and an example of calculation for one time step is given. The proposed method is simple nonlinear parabolic equation, quasilinear heat transfer, explicit
References
Samarskiy A.A. Teoriya raznostnykh skhem. – M.: Nauka, 1989. 2. Galaktionov V.A., Kurdyumov S.P. Metody nelineynogo analiza v zadachakh teploprovodnosti. – M.: Izd-vo Mosk. un-ta, 1985. 3. Martinson L.K. Chislennoe reshenie kvazilineynogo uravneniya teploprovodnosti // Inzhenerno-fizicheskiy zhurnal. – 1995. – T.68, №4. – S. 621–627. 4. Gerenshteyn A.V., Khayrislamov M.Z. Explicit difference scheme for the solution of one-dimensional quasi-linear heat conductivity equation // Vestnik YuUrGU. Ser. Matematika. Mekhanika. Fizika. – 2013. – V.5, №1. – P. 12–17. 5.Jo'rayev G'.U., Xudoyberganov M.O'., Baxramov S.A. Ayirmali sxemalar Kvazichiziqli tenglamada issiqlik o'tkazuvchanlik koeffisienti temperaturaning darajali funksiyasi bo'lganda oshkormas iterasiya sxemasi bilan approksimasiyalash dasturiy ta'minoti // O`zb. Res. Intellektual mulk agentligi. Guvohnoma №DGU 08368, 2020.
