Details

Autor(en) / Beteiligte

• Samarskii, A. A
• Matus, P. P
• Vabishchevich, P. N

Titel

Difference Schemes with Operator Factors [Elektronische Ressource]

Ist Teil von

• Mathematics and Its Applications : 546

Ort / Verlag

Dordrecht : Springer Netherlands

Erscheinungsjahr

2002

Link zu anderen Inhalten

• Volltext

Beschreibungen/Notizen

• Two-and three-level difference schemes for discretisation in time, in conjunction with finite difference or finite element approximations with respect to the space variables, are often used to solve numerically nonstationary problems of mathematical physics. In the theoretical analysis of difference schemes our basic attention is paid to the problem of stability of a difference solution (or well posedness of a difference scheme) with respect to small perturbations of the initial conditions and the right hand side. The theory of stability of difference schemes develops in various directions. The most important results on this subject can be found in the book by A.A. Samarskii and A.V. Goolin [Samarskii and Goolin, 1973]. The survey papers of V. Thomee [Thomee, 1969, Thomee, 1990], A.V. Goolin and A.A. Samarskii [Goolin and Samarskii, 1976], E. Tadmore [Tadmor, 1987] should also be mentioned here. The stability theory is a basis for the analysis of the convergence of an approximative solution to the exact solution, provided that the mesh width tends to zero. In this case the required estimate for the truncation error follows from consideration of the corresponding problem for it and from a priori estimates of stability with respect to the initial data and the right hand side. Putting it briefly, this means the known result that consistency and stability imply convergence