Abrashin, V. N.; Shkel’, V. A. On a class of difference schemes for multi-dimensional nonlinear heat conduction problems. (Russian. English summary) Zbl 0579.65105 Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk 1983, No. 4, 3-8 (1983). The author studies the Cauchy-Dirichlet problem for a multidimensional quasilinear equation of parabolic type by means of a nonlinear difference scheme for which a difference conservation law is fulfilled. Convergence and stability of the proposed scheme are proved. Reviewer: S.F.Sburlan Cited in 1 Review MSC: 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations Keywords:nonlinear heat conduction; Cauchy-Dirichlet problem; nonlinear difference scheme; conservation law; Convergence; stability PDFBibTeX XMLCite \textit{V. N. Abrashin} and \textit{V. A. Shkel'}, Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk 1983, No. 4, 3--8 (1983; Zbl 0579.65105)