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PUBLICATIONS

Piotr Matus, Professor of Mathematics

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  1. Matus, P.P. and Rychagov, G.P. (1997) Mathematical modelling in biology and medicine: Reference book, Belaruskaya navuka, Minsk, 207 p.. (in Russian).
  2. Samarskii A.A., Matus, P.P., and Vabishchevich, P.N., (2002) Difference schemes with operator factors, Kluwer Academic Publishers, Boston/Dordrecht/London, 384 p.

  1. Matus, P.P., Irkhin, U. and Lapinska-Chrzczonowicz, M. (2005) Exact difference schemes for time-dependent problems. Comput. Meth. Appl. Math., 5(4): 422�448.
  2. Matus, P.P., Irkhin, U., Lapinska-Chrzczonowicz, M. and Lemeshevsky S.V.(2006) About exact difference schemes for hyperbolic and parabolic equations. Differ. Uravn. 43(7): 978-986 (In Russian).
  3. Kruk, A., Matus, P.(2007) High accuracy difference schemes for nonlinear transfer equation. Exact difference schemes for time-dependent problems. Math. Model. Anal. 12(4): 469�482.
  4. Matus, P., Kolodynska, A. (2007) Exact difference schemes for hyperbolic equations. Comput. Meth. Appl. Math., 7(4): 341�364.
  5. Laspinska-Chrzczonowicz, M., Matus, P.(2008) Exact difference schemes for hyperbolic equations. Int. J. Numer. Anal. Mod. 5(2): 303�319.

  1. Matus, P.P. (2003) Stability of difference schemes for nonlinear time-dependent problems. Comput. Meth. Appl. Math., 3(2): 313-329.
  2. Matus, P. and Martsynkevich, G. (2005) On the stability of a monotone difference scheme for the Burgers equation. Differents. Uravneniya, 41(7): 955-960. (in Russian); transl. in Differential Equations, 41(7): 1003-1009.
  3. Matus, P. Koroleva O., Chuiko, M. (2007) Stability of difference schemes for equations of weakly compressible liquid. Comput. Meth. Appl. Math., 7(3): 208-220.

  1. Samarskii, A.A., Vabishchevich, P.N., and Matus, P.P. (1997) The strong stability of differential-operator and operator-difference schemes. Dokl. Ross. Akad. Nauk, 356(4): 455-457. (in Russian); transl. in Dokl. Math., 56(2): 726-728.
  2. Matus, P.P. and Panaiotova, I.N. (1999) Strong stability of operator-differential equations and operator-difference schemes. Differents. Uravneniya, 35(2): 256-265. (in Russian); transl. in Differential Equations, 35(2): 257-268.
  3. Matus, P.P. and Jovanovich, B.S. (1999) Coefficient stability of operator-difference schemes. Mathematical Modeling and Analysis (MMA), 4: 135-146.
  4. Samarskii, A.A., Gulin A.V., and Matus P.P. (2000) Sufficient conditions of the coefficient stability of operator-difference schemes. Dokl. Ross. Akad. Nauk, 373(3): 304 - 306.
  5. Jovanovich, B.S. and Matus, P.P. (2001) Strong stability of operator-differential equations and operator-difference schemes in norms integral with respect to time. Differents. Uravneniya, 37(7): 950-958. (in Russian); transl. in Differential Equations, 37(7): 998-1008.
  6. Matus P.P. and Panaiotova, I.N. (2001) Coefficient stability of three-layer operator-difference schemes. Zh. Vychisl. Mat. Mat. Fiz. 41(5): 722-731.
  7. Samarskii A.A., Matus, P.P., and Vabishchevich, P.N., (2002) Difference schemes with operator factors, Kluwer Academic Publishers, Boston/Dordrecht/London, 384 p.
  8. Matus, P.P. (2002) The maximum principle and some of its applications. Comp. Meth. Appl. Math., 2(1): 50-91.
  9. Jovanovich, B.S. and Matus, P.P. (2002) Coefficient stability of differential-operator equations of the second order.. Differents. Uravneniya, 38(10): 1371 - 1377.
  10. Bojovich, D.R., Jovanovich, B.S. and Matus, P.P. (2004) On the strong stability of first-order operator-differential equations. Differents. Uravneniya, 40(5): 655-661. (in Russian); transl. in Differential Equations, 40(5): 703-710.
  11. Lemeshevskii, S.V., Matus, P.P. and Naumovich, A.R. (2004) A criterion for coefficient stability. Differents. Uravneniya, 40(7): 978�984. (in Russian); transl. in Differential Equations, 40(7): 1043�1050.
  12. Jovanovich, B., Lemeshevsky, B., Matus, P. and Vabishchevich, P.N. (2006) Stability of solutions of differential-operator and operator-difference equations in the sense of perturbation of operators. Comp. Meth. Appl. Math., 6(3): 269-290.
  13. Jovanovich, B., Matus, P. (2007) Strong stability of operator-difference equations. Int. J. Appl. Math. and Statistics, 10(507): 978�984;

Hydraulic systems
  1. Koldoba, A.V., Poveshchenko, J.A., Matus, P.P., and Chuiko, M.M. (1992) Mathematical modeling of liquid flow in ramified hydraulic systems. Mathematical Modeling, 4(9): 43-54. (in Russian).
Microelectronics
  1. Ananich, S.E, Matus, P.P., and Mozolevski, I.E. (1997) Difference schemes for Bolzmann-Fokker-Planck equation. Mathematical Modeling, 9(1): 99-115. (in Russian).
  2. Komarov, F.F., Mozolevski, I.E., Matus, P.P., and Ananich, S.E. (1997) Distribution of implanted impurities and deposited energy in high-energy ion implantation. Journal of Technical Physics, 67(1): 61-67.
  3. Komarov,F.F., Mozolevski, I.E., Matus, P.P., and Ananich, S.E. (1997) Distribution of implanted impurities and deposited energy in high-energy ion implantation. Nucl. Instr. and Meth. B 97 (124): 478-483.
Biology and Medicine
  1. Matus, P.P. and Rychagov, G.P. (1997) Mathematical modelling in biology and medicine: Reference book, Belaruskaya navuka, Minsk, 207 p.. (in Russian).
Nonlinear Thermoelasticity: Modelling Matherials with Shape Memory
  1. Melnik, R.V.N., Wang, L., Matus, P. and Rybak, I. (2003) Computational aspects of conservative difference schemes for shape memory alloys applications, Lecture Notes in Computer Science, 2668, 791-800.
  2. Matus, P., Melnik, R.V.N., Wang, L., and Rybak, I. (2004) Nonlinear thermoelasticity: modelling matherials with shape memory Mathematics and Computers in Simulation, 65, 489-509.
Software for planning and construction of dental bridges under performing orthopedic operation in stomatology
Dynamic simulator for training for operators controlling installation of HCVG on the basis of mathematical modelling of the evolutional process of performance of hydroconversion (section of HydroConversion of Vacuum Gas-oil)

  1. Ananich, C.E, Matus, P.P. and Mozolevski, I.E. (1997) Difference schemes for Bolzmann-Fokker-Planck equation.. Mathematical Modeling, 9(1): 99-115.
  2. Samarskii, A.A., Matus, P.P., and Rychagov, V.G. (1997) Monotone difference schemes of high order on nonuniform grids. Mathematical Modeling, 9(2): 95-96. (in Russian).
  3. Samarskii, A.A., Vabishchevich, P.N., and Matus, P.P. (1997) Stability of vector additive schemes. Dokl. Ross. Akad. Nauk, 361(6): 746-748. (in Russian); transl. in Dokl. Math., 58(1): 133-135.
  4. Matus, A.P. and Matus, P.P. (2001) The maximum principle and its application for the investigation of stability and convergence of difference schemes. Mathematical Modeling and Analysis (MMA), 6(2): 289-299.
  5. Matus, P.P. (2002) The maximum principle and some of its applications. Comp. Meth. Appl. Math., 2(1): 50-91.
  6. Matus, P.P. and Rybak, I.V. Monotone difference schemes for nonlinear parabolic equations Differents. Uravneniya, 39(7): 960-968. (in Russian); transl. in Differential Equations, 39(7): 1013-1022.
  7. Matus, P. and Martsynkevich, G. (2004) Monotone and economical difference schemes on non-uniform grids for multidimensional parabolic equations with boundary conditions of the third kind. Comp. Meth. Appl. Math, 4(3): 350-367
  8. Matus, P. and Rybak, I. (2004) Difference schemes for elliptic equations with mixed derivatives. Comp. Meth. Appl. Math, 4(4): 494-505

  1. Vabishchevich, P.N., Matus, P.P., and Shcheglik, V.S. (1994) Operator-difference equations of divergent type. Differents. Uravneniya, 30(7): 1175-1186. (in Russian); transl. in Differential Equations, 30(7): 1088-1100.
  2. Samarskii, A.A., Matus, P.P., and Vabishchevich, P.N. (1998) Stability and convergence of two-level difference schemes in integral with respect to time norms. M3AS: Mathematical Models and Methods in Applied Sciences, 8(6): 1055-1070.
  3. Samarskii, A.A., Vabishchevich, P.N., and Matus, P.P. (1998) Stability of vector additive schemes. Dokl. Ross. Akad. Nauk, 361(6): 746-748. (in Russian); transl. in Dokl. Math., 58(1): 133-135.
  4. Korzyuk, V.I., Lemeshevsky, S.V., and Matus, P.P. (1999) Conjugation problem about jointly separate flow of viscoelastic and viscous fluids in the plane duct. Math. Model. and Analys. (MMA), 4: 114-123.
  5. Mazhukin, V.I., Matus, P.P., and Mikhailyuk, I.A. (2000) Finite-difference schemes for the Korteweg-de Vries equation. Differents. Uravneniya, 36(5): 709-716. (in Russian); transl. in Differential Equations, 36(5): 789-797.
  6. Jovanovich, B.S. and Matus, P.P. (2001) Strong stability of operator-differential equations and operator-difference schemes in norms integral with respect to time. Differents. Uravneniya, 37(7): 950-958. (in Russian); transl. in Differential Equations, 37(7): 998-1008.
  7. Matus, P.P. and Zjuzina, E.L. (2001) Three-level difference schemes on non-uniform in time grids. Comput. Meth. Appl. Math., 1(3): 265-284.
  8. Samarskii A.A., Matus, P.P., and Vabishchevich, P.N., (2002) Difference schemes with operator factors, Kluwer Academic Publishers, Boston/Dordrecht/London, 384 p.
  9. Jovanovich, B., Lemeshevsky, B., and Matus, P. (2002) On the stability of differential-operator equations and operator-difference schemes as t � �. Comp. Meth. Appl. Math., 2(2): 153-170.
  10. Jovanovich, B.S. and Matus, P.P. (2003) Asymptotic Stability of First- and Second-Order Operator-Differential Equations Differents. Uravneniya, 39(3): 383-392. (in Russian); transl. in Differential Equations, 39(3): 414-425.
  11. Bojovich, D.R., Jovanovich, B.S. and Matus, P.P. (2004) On the strong stability of first-order operator-differential equations. Differents. Uravneniya, 40(5): 655-661. (in Russian); transl. in Differential Equations, 40(5): 703-710.
  12. Lemeshevskii, S.V., Matus, P.P. and Naumovich, A.R. (2004) A criterion for coefficient stability. Differents. Uravneniya, 40(7): 978�984. (in Russian); transl. in Differential Equations, 40(7): 1043�1050.
  13. Jovanovich, B., Lemeshevsky, B., Matus, P. and Vabishchevich, P.N. (2006) Stability of solutions of differential-operator and operator-difference equations in the sense of perturbation of operators. Comp. Meth. Appl. Math., 6(3): 269-290.

  1. Abrashin, V.N. and Matus, P.P. (1978) Difference methods for nonlinear hyperbolic equations with piecewise-smooth solutions. Differents. Uravneniya, 14(12): 2223-2240. (in Russian); transl. in Differential Equations, 14(12): 1576-1589.
  2. Abrashin, V.N. and Matus, P.P. (1979) Difference methods for nonlinear hyperbolic equations with piecewise-smooth solutions. II. Differents. Uravneniya, 15(7): 1225-1239. (in Russian); transl. in Differential Equations, 15(7): 870-881.
  3. Matus, P.P. (1980) On convergence of difference schemes for one-dimensional gasdynamics. PhD thesis, Minsk: 124 p.. (in Russian).
  4. Abrashin, V.N. and Matus, P.P. (1981) Accuracy of finite-difference schemes for one-dimensional gasdynamics. Differents. Uravneniya, 17(7): 1155-1170. (in Russian); transl. in Differential Equations, 17(7): 731-744.
  5. Matus, P.P. and Shavel', A.N. (1984) Convergence of finite-difference schemes for one-dimensional gasdynamics problems with thermal conductivity. Differents. Uravneniya, 19(7): 1251-1261. (in Russian); transl. in Differential Equations, 19(7): 932-941.
  6. Matus, P.P. (1985) Unconditional convergence of some finite-difference schemes for gasdynamics problems. Differents. Uravneniya, 21(7): 1227-1238. (in Russian); transl. in Differential Equations, 21(7): 839-848.
  7. Matus, P.P. and Stanishevskaya, L.I. (1991) Uncondotional convergence of difference schemes for nonstationary quasilinear equations of mathematical physics. Differents. Uravneniya, 27(7): 1203-1219. (in Russian); transl. in Differential Equations, 27(11): 847-859.
  8. Vabishchevich, P.N., Matus, P.P., and Rychagov, V.G. (1995) A class of difference schemes on dynamic locally concentrating grids. Differents. Uravneniya, 31(5): 849-857. (in Russian); transl. in Differential Equations, 31(5): 787-796.
  9. Matus, P.P., Moskal'kov, M.N., and Tscheglik, V.S. (1995) Consistent estimates of the convergence rate for the grid method in the case of a second-order nonlinear equation with generalized solutions. Differents. Uravneniya, 31(7): 1219-1226. (in Russian); transl. in Differential Equations, 31(7): 1198-1207.
  10. Jovanovich, B.S., Matus, P.P., and Tscheglik, V.S. (1999) On accuracy of difference schemes for nonlinear parabolic equations with generalized solutions. Zh. Vychisl. Mat. Mat. Fiz., 39(10): 1679-1686. (in Russian); transl. in Comp. Math. Math. Phys., 39(10): 1611-1618.
  11. Jovanovich, B.S., Matus, P.P., and Tscheglik, V.S. (2000) The estimates of accuracy of difference schemes for the nonlinear heat equation with weak solutions. Mathematical Modeling and Analysis (MMA), 5: 86-96.

  1. Samarskii, A.A., Mazhukin, V.I., and Matus, P.P. (1997) $L_2$-conservative schemes for the Korteweg-de Vries equation. Dokl. Ross. Akad. Nauk, 357(4): 458-461. (in Russian); transl. in Dokl. Math., 56(3): 909-912.
  2. Mazhukin, V.I., Matus, P.P., and Mikhailyuk, I.A. (2000) Finite-difference schemes for the Korteweg-de Vries equation. Differents. Uravneniya, 36(5): 709-716. (in Russian); transl. in Differential Equations, 36(5): 789-797.
  3. Samarskii A.A., Matus, P.P., and Vabishchevich, P.N., (2002) Difference schemes with operator factors, Kluwer Academic Publishers, Boston/Dordrecht/London, 384 p.
  1. Vabishchevich, P.N., Lemeshevskij, S.V., and Matus, P.P. (1998) Difference schemes for the problem of fusing hyperbolic and parabolic equations. Sib. Mat. Zh., 39(4): 854-962. (in Russian); transl. in Sib. Math. J., 39(4): 825-834.
  2. Samarskii, A.A., Korzyuk, V.I., Lemeshevskij, S.V., and Matus, P.P. (1998) Difference schemes for the conjugation problem of a hyperbolic and a parabolic equation on moving grids. Dokl. Ross. Akad. Nauk, 361(3): 321-324. (in Russian); transl. in Dokl. Math., 58(1): 74-77.
  3. Korzyuk, V.I., Lemeshevsky, S.V., and Matus, P.P. (1999) Conjugation problem about jointly separate flow of viscoelastic and viscous fluids in the plane duct. Math. Model. and Analys. (MMA), 4: 114-123.
  4. Samarskii, A.A., Korzyuk, V.I., Lemeshevsky, S.V., and Matus, P.P. (2000) Finite-difference methods for problem of conjugation of hyperbolic and parabolic equations. M3AS: Mathematical Models and Methods in Applied Sciences, 10(3): 361-378.

  1. Jovanovich, B., Lemeshevsky, B., and Matus, P. (2002) On the stability of differential-operator equations and operator-difference schemes as t � �. Comp. Meth. Appl. Math., 2(2): 153-170.
  2. Jovanovich, B.S. and Matus, P.P. (2003) Asymptotic Stability of First- and Second-Order Operator-Differential Equations Differents. Uravneniya, 39(3): 383-392. (in Russian); transl. in Differential Equations, 39(3): 414-425.

  1. Matus, P.P. (1990) A class of difference schemes on composite meshes for nonstationary problems of mathematical physics. Differents. Uravneniya, 26(7): 1241-1254. (in Russian); transl. in Differential Equations, 26(7): 911-922.
  2. Matus, P.P. (1991) Construction of difference schemes for multidimensional parabolic equations. Differents. Uravneniya, 27(11): 1961-1971. (in Russian); transl. in Differential Equations, 27(11): 1404-1414.
  3. Matus, P.P. (1993) Conservative finite-difference scheme in subdomains for parabolic and hyperbolic second-order equations. Differents. Uravneniya, 29(4): 700-711. (in Russian); transl. in Differential Equations, 29(4): 595-605.
  4. Matus, P.P. (1993) Conservative difference schemes for quasilinear parabolic equations in subdomains. Differents. Uravneniya, 29(7): 1222-1231. (in Russian); transl. in Differential Equations, 29(7): 1060-1069.
  5. Matus, P.P. and Mikhailuk, I.A. (1993) Difference schemes with variable weights for evolutionary equations of second order. Mathematical Modeling, 5(12): 35-60. (in Russian).
  6. Matus, P.P. (1994) Difference schemes on composite grids for hyperbolic equations. Zh. Vychisl. Mat. Mat. Fiz. 34(6): 870-885; transl. in Comput. Math. Math. Phys., 34(6): 749-761.
  7. Vabishchevich, P.N., Matus, P.P., and Rychagov, V.G. (1995) A class of difference schemes on dynamic locally concentrating grids. Differents. Uravneniya, 31(5): 849-857. (in Russian); transl. in Differential Equations, 31(5): 787-796.
  8. Samarskii, A.A., Vabishchevich, P.N., and Matus, P.P. (1996) Finite-difference approximations of higher accuracy order on nonuniform grids. Differents. Uravneniya, 32(2): 265-274. (in Russian); transl. in Differential Equations, 32(2): 269-281.
  9. Samarskii, A.A., Mazhukin, V.I., Matus, P.P., and Chuiko, M.M. (1996) Invariant finite-difference schemes for equations of mathematical physics in nonstationary coordinate systems. Differents. Uravneniya, 32(12): 1691-1701. (in Russian); transl. in Differential Equations, 32(12): 1685-1695.
  10. Samarskii, A.A., Matus, P.P., and Rychagov, V.G. (1997) Monotone difference schemes of high order on nonuniform grids. Mathematical Modeling, 9(2): 95-96. (in Russian).
  11. Samarskii, A.A., Mazhukin, V.I., and Matus, P.P. (1997) Invariant difference schemes for differential equations with the transformation of independent variables. Dokl. Ross. Akad. Nauk, 352(5): 602-605; transl. in Dokl. Math., 55(1): 140-143.
  12. Samarskii, A.A., Jovanovich, B.S., Matus, P.P., and Shcheglik, V.S. (1997) Finite-difference schemes on adaptive time grids for parabolic equations with generalized solutions. Differents. Uravneniya, 33(7): 975-984. (in Russian); transl. in Differential Equations, 33(7): 981-991.
  13. Samarskii, A.A., Vabishchevich, P.N., and Matus, P.P. (1998) Second-order accurate finite-difference schemes on nonuniform grids. Zh. Vychisl. Mat. Mat. Fiz., 38(3): 413-424. (in Russian); transl. in Comput. Math. Math. Phys., 38(3): 399-410.
  14. Vabishchevich, P.N., Lemeshevskij, S.V., and Matus, P.P. (1998) Difference schemes for the problem of fusing hyperbolic and parabolic equations. Sib. Mat. Zh., 39(4): 854-962. (in Russian); transl. in Sib. Math. J., 39(4): 825-834.
  15. Samarskii, A.A., Mazhukin, V.I., and Matus, P.P. (1998) Finite-difference scheme on nonuniform grids for a two-dimensional parabolic equation. Differents. Uravneniya, 34(7): 980-987. (in Russian); transl. in Differ. Equations, 34(7): 982-990.
  16. Jovanovich, B.S. and Matus, P.P. (1999) Estimation of the convergence rate of difference schemes for elliptic problems. Zh. Vychisl. Mat. Mat. Fiz., 39(1): 61-69. (in Russian); transl. in Comp. Math. Math. Phys., 39(1): 56-64.
  17. Samarskii, A.A., Mazhukin, V.I., Malafei, D.A., and Matus, P.P. (1999) Accuracy enhancement in difference schemes on spatially nonuniform grids. Dokl. Ross. Akad. Nauk, 367(3): 310-313. (in Russian); transl. in Dokl. Math. 60(1): 61-64.
  18. Zyl, A.N. and Matus, P.P. (1999) Efficient high-order accurate finite-difference schemes for multidimensional parabolic equations on nonuniform grids. Zh. Vychisl. Mat. Mat. Fiz., 39(7): 1151-1157. (in Russian); transl. in Comp. Math. Math. Phys., 39(7): 1109-1115.
  19. Samarskii, A.A., Vabishchevich, P.N., Zyl, A.N., and Matus, P.P. (1999) Difference scheme of second order accuracy for Dirichlet problem in a general domain. Math. Modeling, 11(9): 71-82. (in Russian).
  20. Matus, P.P. and Zyl, A.N. (2000) Difference schemes of high order accuracy for mathematical physics problems in arbitrary areas. Mathematical Modeling and Analysis (MMA), 5: 133-142.
  21. Matus, A.P. and Matus, P.P. (2001) The maximum principle and its application for the investigation of stability and convergence of difference schemes. Mathematical Modeling and Analysis (MMA), 6(2): 289-299.
  22. Matus, P.P. and Zjuzina, E.L. (2001) Three-level difference schemes on non-uniform in time grids. Comput. Meth. Appl. Math., 1(3): 265-284.
  23. Samarskii A.A., Matus, P.P., and Vabishchevich, P.N., (2002) Difference schemes with operator factors, Kluwer Academic Publishers, Boston/Dordrecht/London, 384 p.
  24. Matus, P.P. (2002) The maximum principle and some of its applications. Comput. Meth. Appl. Math., 2(1): 50-91.
  25. Matus, P. and Martsynkevich, G. (2004) Monotone and economical difference schemes on non-uniform grids for multidimensional parabolic equations with boundary conditions of the third kind. Comp. Meth. Appl. Math, 4(3): 350-367
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