The perturbation algorithm for the realization of a four-layer semi-discrete solution scheme of an abstract evolutionary problem

References

[1] V. I. Agoshkov and D. V. Gulua, A Perturbation Algorithm for Realization of Finite-Dimensional Realization Problems (in Russian), Akad. Nauk SSSR, Moscow, 1990. Search in Google Scholar

[2] A. Ashyralyev and P. E. Sobolevskiĭ, New Difference Schemes for Partial Differential Equations, Oper. Theory Adv. Appl. 148, Birkhäuser, Basel, 2004. 10.1007/978-3-0348-7922-4Search in Google Scholar

[3] A. Ashyralyev and P. E. Sobolevskiĭ, Well-Posedness of Parabolic Difference Equations, Oper. Theory Adv. Appl. 69, Birkhäuser, Basel, 1994. 10.1007/978-3-0348-8518-8Search in Google Scholar

[4] N. Y. Bakaev, Linear Discrete Parabolic Problems, North-Holland Math. Stud. 203, Elsevier Science, Amsterdam, 2006. Search in Google Scholar

[5] M. Crouzeix, Une méthode multipas implicite-explicite pour l’approximation des équations d’évolution paraboliques, Numer. Math. 35 (1980), no. 3, 257–276. 10.1007/BF01396412Search in Google Scholar

[6] M. Crouzeix and P.-A. Raviart, Approximation des équations d’évolution linéaires par des méthodes à pas multiples, C. R. Acad. Sci. Paris Sér. A 28 (1976), no. 6, 367–370. Search in Google Scholar

[7] S. K. Godunov and V. S. Ryaben’kiĭ, Difference Schemes. Introduction to the Theory. Second Edition, Revised and Augmented (in Russian), Izdat. “Nauka”, Moscow, 1977. Search in Google Scholar

[8] N. N. Janenko, The Method of Fractional Steps for Solving Multidimensional Problems of Mathematical Physics (in Russian), Izdat. “Nauka” Sibirsk. Otdel., Novosibirsk, 1967. Search in Google Scholar

[9] L. V. Kantorovich and G. P. Akilov, Functional Analysis, 2nd ed. (in Russian), Izdat. “Nauka”, Moscow, 1977. Search in Google Scholar

[10] T. Kato and T. Kato, Perturbation Theory for Linear Operators (in Russian), Izdat. “Mir”, Moscow, 1972. Search in Google Scholar

[11] G. I. Marchuk, Methods of Computational Mathematics (in Russian), Izdat. “Nauka” Sibirsk. Otdel., Novosibirsk, 1973. Search in Google Scholar

[12] G. I. Marchuk, V. I. Agoshkov and V. P. Shutyaev, Adjoint Equations and Perturbation Methods in Nonlinear Problems of Mathematical Physics (in Russian), VO “Nauka”, Moscow, 1993. Search in Google Scholar

[13] G. I. Marchuk and V. V. Shaĭdurov, Difference Methods and Their Extrapolations, Appl. Math. (New York) 19, Springer, New York, 1983. 10.1007/978-1-4613-8224-9Search in Google Scholar

[14] V. Pereyra, On improving an approximate solution of a functional equation by deferred corrections, Numer. Math. 8 (1966), 376–391. 10.1007/BF02162981Search in Google Scholar

[15] V. Pereyra, Accelerating the convergence of discretization algorithms, SIAM J. Numer. Anal. 4 (1967), 508–533. 10.1137/0704046Search in Google Scholar

[16] S. Piskarev, Differential Equations in Banach Space and Their Aproximation (in Russian), Moscow State University, Moscow, 2005. Search in Google Scholar

[17] S. Piskarev and H. Zwart, Crank–Nicolson scheme for abstract linear systems, Numer. Funct. Anal. Optim. 28 (2007), no. 5–6, 717–736. 10.1080/01630560701380981Search in Google Scholar

[18] R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems 2nd ed., Interscience Tracts Pure Appl. Math. 4, John Wiley & Sons, New York, 1967. Search in Google Scholar

[19] D. L. Rogava, Semidiscrete Schemes for Operator Differential Equations (in Russian), Izdatel’stvo “Tekhnicheskogo Universitet”, Tbilisi, 1995. Search in Google Scholar

[20] D. L. Rogava and D. V. Gulua, A perturbation algorithm for realizing finite-difference approximation of an abstract evolution problem, and an explicit error estimate of the approximate solution, Dokl. Akad. Nauk 456 (2014), no. 4, 405–407. Search in Google Scholar

[21] J. Rogava and D. Gulua, Reduction of a three-layer semi-discrete scheme for an abstract parabolic equation to two-layer schemes. Explicit estimates for the approximate solution error (in Russian), Sovrem. Mat. Prilozh. 89 (2013); translation in J. Math. Sci. (N.Y.) 206 (2015), no. 4, 424–444. 10.1007/s10958-015-2322-8Search in Google Scholar

[22] E. Rothe, Über die Wärmeleitungsgleichung mit nichtkonstanten Koeffizienten im räumlichen Falle, Math. Ann. 104 (1931), no. 1, 340–354. 10.1007/BF01457942Search in Google Scholar

[23] A. A. Samarskiĭ, Theory of Difference Schemes (in Russian), Izdat. “Nauka”, Moscow, 1977. Search in Google Scholar