Vabishchevich, P. N. Works of A. A. Samarskii on computational mathematics. (English) Zbl 1162.65053 Comput. Methods Appl. Math. 9, No. 1, 5-36 (2009). Summary: This is a review of the main results in computational mathematics that were obtained by the eminent Russian mathematician Alexander Andreevich Samarskii (February 19, 1919 - February 11, 2008). His outstanding research output addresses all the main questions that arise in the construction and justification of algorithms for the numerical solution of problems from mathematical physics. The remarkable works of A. A. Samarskii include statements of the main principles required in the construction of difference schemes, rigorous mathematical proofs of the stability and convergence of these schemes, and also investigations of their algorithmic implementation. A. A. Samarskii and his collaborators constructed and applied in practical calculations a large number of algorithms for solving various problems from mathematical physics, including thermal physics, gas dynamics, magnetic gas dynamics, plasma physics, ecology and other important models from the natural sciences. MSC: 65N06 Finite difference methods for boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 76M20 Finite difference methods applied to problems in fluid mechanics 80M20 Finite difference methods applied to problems in thermodynamics and heat transfer 65-03 History of numerical analysis 01A61 History of mathematics in the 21st century Keywords:finite difference method; operator-difference scheme; stability; additive scheme; splitting scheme; iterative method; Alexander Andreevich Samarskii; convergence; mathematical physics; thermal physics; gas dynamics; plasma physics; ecology PDFBibTeX XMLCite \textit{P. N. Vabishchevich}, Comput. Methods Appl. Math. 9, No. 1, 5--36 (2009; Zbl 1162.65053) Full Text: DOI