Samarskij, A. A.; Vabishchevich, P. N. Regularized additive full approximation schemes. (English. Russian original) Zbl 0959.65099 Dokl. Math. 57, No. 1, 83-86 (1998); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 358, No. 4, 461-464 (1998). From the introduction: Additive difference schemes for first- and second-order differential-operator equations are constructed in the general case of additive splitting with an arbitrary number of mutually noncommuting operator terms. The construction of unconditionally stable schemes is based on regularization of a simplest explicit two- or three-layer scheme by a small multiplicative perturbation of each splitting operator. This approach covers the basic classes of nonstationary problems of mathematical physics. Cited in 6 Documents MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 34G10 Linear differential equations in abstract spaces 35K15 Initial value problems for second-order parabolic equations 65J10 Numerical solutions to equations with linear operators 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs Keywords:stability; evolution equation; Cauchy problem; additive difference schemes; first- and second-order differential-operator equations; additive splitting; regularization PDFBibTeX XMLCite \textit{A. A. Samarskij} and \textit{P. N. Vabishchevich}, Dokl. Math. 57, No. 1, 461--464 (1998; Zbl 0959.65099); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 358, No. 4, 461--464 (1998)