Lazurchak, I. I.; Makarov, V. L. A two-sided FD-method for the Dirichlet problem for the Helmholtz equation. (English. Russian original) Zbl 0937.65124 Differ. Equations 35, No. 3, 391-398 (1999); translation from Differ. Uravn. 35, No. 3, 388-395 (1999). Reviewer: W.Heinrichs (Essen) MSC: 65N35 65N15 35J05 PDFBibTeX XMLCite \textit{I. I. Lazurchak} and \textit{V. L. Makarov}, Differ. Equations 35, No. 3, 391--398 (1999; Zbl 0937.65124); translation from Differ. Uravn. 35, No. 3, 388--395 (1999)
Makarov, V. L.; Makarov, S. V.; Moskal’kov, M. M. A fast algorithm for solving the Dirichlet problem on hexagonal templet for the Poisson equation in a rectangle. (English. Ukrainian original) Zbl 0839.65109 J. Math. Sci., New York 77, No. 5, 3410-3414 (1995). MSC: 65N06 65N22 65F05 65T50 35J05 PDFBibTeX XMLCite \textit{V. L. Makarov} et al., Obchisl. Prikl. Mat. 77, 19--26 (1993; Zbl 0839.65109) Full Text: DOI
Makarov, V. L.; Makarov, S. V.; Moskal’kov, M. N. A fast algorithm for solving the difference Dirichlet problem on a hexagonal pattern for the Poisson equation in a rectangle. (Ukrainian) Zbl 0833.65116 Obchisl. Prikl. Mat. 77, 19-26 (1993). MSC: 65N06 65N22 65F05 65T50 35J05 PDFBibTeX XMLCite \textit{V. L. Makarov} et al., Obchisl. Prikl. Mat. 77, 19--26 (1993; Zbl 0833.65116)
Vojtsekhovskij, S. A.; Makarov, V. L. Difference schemes for the Dirichlet problem for an elliptic equation with discontinuous coefficients in an arbitrary region on a regular grid. (English. Russian original) Zbl 0723.65082 J. Sov. Math. 54, No. 2, 747-751 (1991); translation from Vychisl. Prikl. Mat., Kiev 56, 3-7 (1985). MSC: 65N12 65N06 35J25 PDFBibTeX XMLCite \textit{S. A. Vojtsekhovskij} and \textit{V. L. Makarov}, J. Sov. Math. 54, No. 2, 747--751 (1991; Zbl 0723.65082); translation from Vychisl. Prikl. Mat., Kiev 56, 3--7 (1985) Full Text: DOI
Voitsekhovskii, S. A.; Makarov, V. L.; Rybak, Yu. I. Rate-of-convergence bounds of a finite-difference approximation of the Dirichlet problem for the Helmholtz equation with a coefficient from the “negative” space. (English. Russian original) Zbl 0837.65115 J. Math. Sci., New York 71, No. 4, 2531-2538 (1994); translation from Vychisl. Prikl. Mat. 72, 3-11 (1990). MSC: 65N12 65N06 35J05 PDFBibTeX XMLCite \textit{S. A. Voitsekhovskii} et al., J. Math. Sci., New York 71, No. 4, 1 (1990; Zbl 0837.65115); translation from Vychisl. Prikl. Mat. 72, 3--11 (1990) Full Text: DOI
Vojtsekhovskij, S. A.; Makarov, V. L.; Rybak, Yu. I. Estimates of the convergence rate of difference approximations of the Dirichlet problem for the equation \(-\Delta u+\sum _{|\alpha|\leq 1}(-1)^{|\alpha|}D^{\alpha}q_{\alpha}(x)u=f(x)\) when \(q_{\alpha}(x)\in W_{\infty}^{\lambda|\alpha|}(\Omega)\), \(\lambda\in (0,1]\). (English. Russian original) Zbl 0671.65081 Differ. Equations 24, No. 11, 1338-1344 (1988); translation from Differ. Uravn. 24, No. 11, 1987-1994 (1988). MSC: 65N12 65N15 35J05 PDFBibTeX XMLCite \textit{S. A. Vojtsekhovskij} et al., Differ. Equations 24, No. 11, 1338--1344 (1988; Zbl 0671.65081); translation from Differ. Uravn. 24, No. 11, 1987--1994 (1988)
Makarov, V. L.; Karalashvili, L. Sh. On some approach to the construction of a straight line method scheme of high-order accuracy. (Russian. English summary) Zbl 0662.65102 Soobshch. Akad. Nauk Gruz. SSR 131, No. 1, 33-36 (1988). Reviewer: I.Evzerov MSC: 65N40 35J05 PDFBibTeX XMLCite \textit{V. L. Makarov} and \textit{L. Sh. Karalashvili}, Soobshch. Akad. Nauk Gruz. SSR 131, No. 1, 33--36 (1988; Zbl 0662.65102)
Voĭtsekhovskiĭ, S. A.; Makarov, V. L.; Rybak, Yu. I. Estimates of the convergence rate of difference approximations of the Dirichlet problem for the equation \(-\Delta u+\sum _{|\alpha|\leq 1}(-1)^{|\alpha|}D^{\alpha}q_{\alpha}(x)u=f(x)\) for \(q_{\alpha}(x)\in W_{\infty}^{\lambda|\alpha|}(\Omega)\), \(\lambda\) \(\in (0,1]\). (Russian) Zbl 0657.65112 Differ. Uravn. 24, No. 11, 1987-1994 (1988). Reviewer: J.Vaníček MSC: 65N12 65N15 35J05 PDFBibTeX XMLCite \textit{S. A. Voĭtsekhovskiĭ} et al., Differ. Uravn. 24, No. 11, 1987--1994 (1988; Zbl 0657.65112)
Makarov, V. L.; Ryzhenko, A. I. Rate-of-convergence bounds of the grid method for the axisymmetric Dirichlet problem in spherical geometry. (English. Russian original) Zbl 0792.65082 J. Sov. Math. 66, No. 2, 2156-2158 (1993); translation from Vychisl. Prikl. Mat., Kiev 63, 38-42 (1987). MSC: 65N12 65N06 35J05 PDFBibTeX XMLCite \textit{V. L. Makarov} and \textit{A. I. Ryzhenko}, J. Sov. Math. 66, No. 2, 1 (1987; Zbl 0792.65082); translation from Vychisl. Prikl. Mat., Kiev 63, 38--42 (1987)
Makarov, V. L.; Ryzhenko, A. I. Estimates of the convergence rate of the difference method for the axially symmetric Dirichlet problem in spherical geometry. (Russian) Zbl 0726.65112 Vychisl. Prikl. Mat., Kiev 63, 38-42 (1987). MSC: 65N12 65N06 35J05 PDFBibTeX XMLCite \textit{V. L. Makarov} and \textit{A. I. Ryzhenko}, Vychisl. Prikl. Mat. 63, 38--42 (1987; Zbl 0726.65112)
Makarov, V. L.; Ryzhenko, A. I. Compatible convergence-rate estimates of the mesh method for the axisymmetric Poisson equation in spherical coordinates. (English. Russian original) Zbl 0664.65099 U.S.S.R. Comput. Math. Math. Phys. 27, No. 4, 195-197 (1987); translation from Zh. Vychisl. Mat. Mat. Fiz. 27, No. 8, 1252-1255 (1987). MSC: 65N12 35J05 PDFBibTeX XMLCite \textit{V. L. Makarov} and \textit{A. I. Ryzhenko}, U.S.S.R. Comput. Math. Math. Phys. 27, No. 4, 195--197 (1987; Zbl 0664.65099); translation from Zh. Vychisl. Mat. Mat. Fiz. 27, No. 8, 1252--1255 (1987) Full Text: DOI
Makarov, V. L.; Ryzhenko, A. I. Matched estimates of the rate of convergence of the net method for Poisson’s equation in polar coordinates. (English. Russian original) Zbl 0655.65111 U.S.S.R. Comput. Math. Math. Phys. 27, No. 3, 147-152 (1987); translation from Zh. Vychisl. Mat. Mat. Fiz. 27, No. 6, 867-874 (1987). MSC: 65N15 65N12 35J05 PDFBibTeX XMLCite \textit{V. L. Makarov} and \textit{A. I. Ryzhenko}, U.S.S.R. Comput. Math. Math. Phys. 27, No. 3, 147--152 (1987; Zbl 0655.65111); translation from Zh. Vychisl. Mat. Mat. Fiz. 27, No. 6, 867--874 (1987) Full Text: DOI
Makarov, V. L.; Ryzhenko, A. I. Compatible estimates for the rate of convergence of the net method for the axially symmetric Poisson equation in spherical coordinates. (English) Zbl 0648.65068 Zh. Vychisl. Mat. Mat. Fiz. 27, No. 8, 1252-1255 (1987). Reviewer: J.Kačur MSC: 65N12 35J05 PDFBibTeX XMLCite \textit{V. L. Makarov} and \textit{A. I. Ryzhenko}, Zh. Vychisl. Mat. Mat. Fiz. 27, No. 8, 1252--1255 (1987; Zbl 0648.65068)
Makarov, V. L.; Ryzhenko, A. I. Coordinated estimates for the convergence rate of the network method for the Poisson equation in polar coordinates. (Russian) Zbl 0633.65094 Zh. Vychisl. Mat. Mat. Fiz. 27, No. 6, 867-874 (1987). Reviewer: D.Fagé MSC: 65N15 65N12 35J05 PDFBibTeX XMLCite \textit{V. L. Makarov} and \textit{A. I. Ryzhenko}, Zh. Vychisl. Mat. Mat. Fiz. 27, No. 6, 867--874 (1987; Zbl 0633.65094)
Vojtsekhovskij, S. A.; Makarov, V. L.; Shablij, T. G. Estimation of the convergence rate of difference solutions to generalized solutions of the Dirichlet problem for the Helmholtz equation of class \(\overset\circ W^ 1_ 2(\Omega)\) in a convex domain. (English. Russian original) Zbl 0607.65059 Ukr. Math. J. 38, 88-90 (1986); translation from Ukr. Mat. Zh. 38, No. 1, 98-101 (1986). MSC: 65N12 65N06 35J05 PDFBibTeX XMLCite \textit{S. A. Vojtsekhovskij} et al., Ukr. Math. J. 38, 88--90 (1986; Zbl 0607.65059); translation from Ukr. Mat. Zh. 38, No. 1, 98--101 (1986) Full Text: DOI
Vojtsekhovskij, S. A.; Makarov, V. L. Difference schemes to solve the Dirichlet problem for an elliptic equation with discontinuous coefficients in an arbitrary region on a regular net. (Russian) Zbl 0634.65082 Vychisl. Prikl. Mat., Kiev 56, 3-7 (1985). MSC: 65N12 65N06 35J25 PDFBibTeX XMLCite \textit{S. A. Vojtsekhovskij} and \textit{V. L. Makarov}, Vychisl. Prikl. Mat. 56, 3--7 (1985; Zbl 0634.65082)
Vojtsekhovskij, S. A.; Makarov, V. L.; Novichenko, V. N. Estimation of the rate of convergence of difference schemes for quasilinear fourth order elliptic equations. (English. Russian original) Zbl 0606.65068 U.S.S.R. Comput. Math. Math. Phys. 25, No. 6, 90-92 (1985); translation from Zh. Vychisl. Mat. Mat. Fiz. 25, No. 11, 1725-1729 (1985). MSC: 65N12 65N06 35J65 PDFBibTeX XMLCite \textit{S. A. Vojtsekhovskij} et al., U.S.S.R. Comput. Math. Math. Phys. 25, No. 6, 90--92 (1985; Zbl 0606.65068); translation from Zh. Vychisl. Mat. Mat. Fiz. 25, No. 11, 1725--1729 (1985) Full Text: DOI
Makarov, V. L.; Ryzhenko, A. I. Difference schemes of second accuracy order on a uniform net for the axisymmetric Poisson problem with solution in the class \(W^ 2_ 2(\Omega)\). (Russian) Zbl 0628.65086 Vychisl. Prikl. Mat., Kiev 49, 43-51 (1983). MSC: 65N12 65N15 35J05 PDFBibTeX XMLCite \textit{V. L. Makarov} and \textit{A. I. Ryzhenko}, Vychisl. Prikl. Mat. 49, 43--51 (1983; Zbl 0628.65086)
Lazarov, R. D.; Makarov, V. L. Difference schemes of second-order precision for the axially symmetric Poisson equation on generalized solutions in \(W_2^2\). (English. Russian original) Zbl 0488.65041 Sov. Math., Dokl. 25, 15-19 (1982); translation from Dokl. Akad. Nauk SSSR 262, 22-26 (1982). MSC: 65N12 65N15 35J05 PDFBibTeX XMLCite \textit{R. D. Lazarov} and \textit{V. L. Makarov}, Sov. Math., Dokl. 25, 15--19 (1982; Zbl 0488.65041); translation from Dokl. Akad. Nauk SSSR 262, 22--26 (1982)
Vojtsekhovskij, S. A.; Makarov, V. L.; Prikazchikov, V. G. A variant of the fictitious-region method in eigenvalue problems. (English. Russian original) Zbl 0437.65080 Differ. Equations 15, 1196-1199 (1980); translation from Differ. Uravn. 15, 1676-1680 (1979). MSC: 65N25 35P15 35J25 PDFBibTeX XMLCite \textit{S. A. Vojtsekhovskij} et al., Differ. Equations 15, 1196--1199 (1980; Zbl 0437.65080); translation from Differ. Uravn. 15, 1676--1680 (1979)
Makarov, V. L.; Gavrilyuk, I. P.; Shmanenko, T. L. On the regularisation of difference schemes for quasilinear elliptic equations in a strip. (Russian) Zbl 0442.65095 Vychisl. Prikl. Mat., Kiev 39, 94-101 (1979). MSC: 65N12 35J65 65N22 65N06 PDFBibTeX XMLCite \textit{V. L. Makarov} et al., Vychisl. Prikl. Mat. 39, 94--101 (1979; Zbl 0442.65095)