Difference Schemes with Operator Factors

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 non­ stationary problems of mathematical physics. In the theoretical analysis of difference schemes our basic attention is paid to the problem of sta­ bility 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 di­ rections. 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. Tad­ more [Tadmor, 1987] should also be mentioned here. The stability theory is a basis for the analysis of the convergence of an approximative solu­ tion 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 es­ timates 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.

This book contains substantially extended and revised versions of the best papers from the 12th International Conference on Enterprise Information Systems (ICEIS 2010), held in Funchal, Madeira, Portugal, June 8-12, 2010.

Two invited papers are presented together with 39 contributions, which were carefully reviewed and selected from 62 full papers presented at the conference (out of 448 submissions). They reflect state-of-the-art research work that is often driven by real-world applications, thus successfully relating the academic with the industrial community. The topics covered are: databases and information systems integration, artificial intelligence and decision support systems, information systems analysis and specification, software agents and internet computing, and human-computer interaction.