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Mat. Zametki, 1969, Volume 6, Issue 2, Pages 237–248 (Mi mz6928)  

This article is cited in 96 scientific papers (total in 98 papers)

Differencing scheme for a differential equation with a small parameter affecting the highest derivative

A. M. Il'in

V. A. Steklov Institute of Mathematics, Sverdlovsk Branch of the Academy of Sciences of USSR

Abstract: A differencing scheme is introduced for a differential equation with a small parameter affecting the highest derivatives. In the case of an ordinary differential equation, the solution of the difference equation is shown to converge uniformly with respect to the small parameter.

Full text: PDF file (665 kB)

English version:
Mathematical Notes, 1969, 6:2, 596–602

Bibliographic databases:

UDC: 518
Received: 17.01.1969

Citation: A. M. Il'in, “Differencing scheme for a differential equation with a small parameter affecting the highest derivative”, Mat. Zametki, 6:2 (1969), 237–248; Math. Notes, 6:2 (1969), 596–602

Citation in format AMSBIB
\Bibitem{Ili69}
\by A.~M.~Il'in
\paper Differencing scheme for a~differential equation with a~small parameter affecting the highest derivative
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 2
\pages 237--248
\mathnet{http://mi.mathnet.ru/mz6928}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=260195}
\zmath{https://zbmath.org/?q=an:0185.42203}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 2
\pages 596--602
\crossref{https://doi.org/10.1007/BF01093706}


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    1. A. B. Vasil'eva, “The development of the theory of ordinary differential equations with a small parameter multiplying the highest derivative during the period 1966–1976”, Russian Math. Surveys, 31:6 (1976), 109–131  mathnet  crossref  mathscinet  zmath
    2. L. A. Kalyakin, “On approximate methods of solving nonlinear boundary value problems with a small parameter”, Math. USSR-Sb., 28:4 (1976), 491–500  mathnet  crossref  mathscinet  zmath  isi
    3. G. I. Shishkin, “Grid approximation of a singularly perturbed boundary-value problem for a quasi-linear elliptic equation in the completely degenerate case”, U.S.S.R. Comput. Math. Math. Phys., 31:12 (1991), 33–46  mathnet  mathscinet  zmath  isi
    4. G. I. Shishkin, “A difference scheme for a singularly perturbed parabolic equation degenerating on the boundary”, Comput. Math. Math. Phys., 32:5 (1992), 621–636  mathnet  mathscinet  zmath  isi
    5. G. I. Shishkin, “A difference approximation of a singularly perturbed boundary-value problem for quasilinear elliptic equations degenerating into first-order equations”, Comput. Math. Math. Phys., 32:4 (1992), 467–480  mathnet  mathscinet  zmath  isi
    6. G. I. Shishkin, “The method of additive separation of singularities for quasilinear singularly perturbed elliptic and parabolic equations”, Comput. Math. Math. Phys., 34:12 (1994), 1541–1558  mathnet  mathscinet  zmath  isi
    7. K. V. Emel'yanov, “Applying optimal difference grids to problems with singular perturbations”, Comput. Math. Math. Phys., 34:6 (1994), 809–814  mathnet  mathscinet  zmath  isi
    8. G. I. Shishkin, “A grid approximation of the method of additive separation of singularities for a singularly perturbed equation of parabolic type”, Comput. Math. Math. Phys., 34:5 (1994), 621–637  mathnet  mathscinet  zmath  isi
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    13. V. B. Andreev, N. V. Kopteva, “A study of difference schemes with the first derivative approximated by a central difference ratio”, Comput. Math. Math. Phys., 36:8 (1996), 1065–1078  mathnet  mathscinet  zmath  isi
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    19. G. I. Shishkin, “Grid approximations of singularly perturbed systems for parabolic convection-diffusion equations with counterflow”, Sib. zhurn. vychisl. matem., 1:3 (1998), 281–297  mathnet  mathscinet  zmath
    20. G. I. Shishkin, “Finite-difference approximations for singularly perturbed elliptic equations”, Comput. Math. Math. Phys., 38:12 (1998), 1909–1921  mathnet  mathscinet  zmath
    21. G. I. Shishkin, “Approximation of singularly perturbed elliptic equations with convective terms in the case of a flow impinging on an impermeable wall”, Comput. Math. Math. Phys., 38:11 (1998), 1768–1782  mathnet  mathscinet  zmath
    22. A. I. Zadorin, “Numerical solution of an equation with a small parameter on an infinite interval”, Comput. Math. Math. Phys., 38:10 (1998), 1602–1614  mathnet  mathscinet  zmath
    23. G. I. Shishkin, “Increasing the accuracy of approximate solutions by residual correction for singularly perturbed equations with convective terms”, Russian Math. (Iz. VUZ), 43:5 (1999), 77–89  mathnet  mathscinet  zmath
    24. N. S. Bakhvalov, “Automatic construction of integration mesh for boundary value problems with boundary layers”, Comput. Math. Math. Phys., 39:8 (1999), 1238–1243  mathnet  mathscinet  zmath
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    64. Comput. Math. Math. Phys., 50:1 (2010), 38–53  mathnet  crossref  mathscinet  elib
    65. A. I. Zadorin, N. A. Zadorin, “Spline interpolation on a uniform grid for a function with a boundary layer component”, Comput. Math. Math. Phys., 50:2 (2010), 211–223  mathnet  crossref  mathscinet  adsnasa  isi
    66. G. I. Shishkin, L. P. Shishkina, “A Richardson scheme of an increased order of accuracy for a semilinear singularly perturbed elliptic convection-diffusion equation”, Comput. Math. Math. Phys., 50:3 (2010), 437–456  mathnet  crossref  mathscinet  adsnasa  isi
    67. G. I. Shishkin, L. P. Shishkina, “A Richardson scheme of the decomposition method for solving singularly perturbed parabolic reaction-diffusion equation”, Comput. Math. Math. Phys., 50:12 (2010), 2003–2022  mathnet  crossref  adsnasa
    68. Kadalbajoo M.K. Gupta V., “A Brief Survey on Numerical Methods for Solving Singularly Perturbed Problems”, Appl. Math. Comput., 217:8 (2010), 3641–3716  crossref  isi
    69. A. I. Zadorin, S. V. Tikhovskaya, “Analysis of a difference scheme for a singular perturbation Cauchy problem on refined grids”, Num. Anal. Appl., 4:1 (2011), 36–45  mathnet  crossref
    70. G. I. Shishkin, L. P. Shishkina, “Improved approximations of the solution and derivatives to a singularly perturbed reaction-diffusion equation based on the solution decomposition method”, Comput. Math. Math. Phys., 51:6 (2011), 1020–1049  mathnet  crossref  mathscinet  isi
    71. A. I. Zadorin, N. A. Zadorin, “Interpolyatsiya funktsii s pogransloinymi sostavlyayuschimi i ee primenenie v dvukhsetochnom metode”, Sib. elektron. matem. izv., 8 (2011), 247–267  mathnet
    72. Igor A. Kuzovatov, Andrei V. Minakov, “Vliyanie effekta Kholla na strukturu tokovogo sloya v kanale lineinogo MGD-uskoritelya”, Zhurn. SFU. Ser. Matem. i fiz., 4:4 (2011), 505–518  mathnet
    73. A. I. Zadorin, S. V. Tihovskaya, “Difference scheme on an uniform mesh for a singularly perturbed Cauchy problem”, J. Math. Sci., 195:6 (2013), 865–872  mathnet  crossref
    74. I. A. Kuzovatov, A. V. Shamshurin, “Chislennoe modelirovanie protsessa orientatsii dvukhurovnevykh molekul vo vneshnem pole pri pomoschi metoda eksponentsialnoi podgonki”, Sib. zhurn. industr. matem., 15:3 (2012), 45–57  mathnet  mathscinet
    75. “Arlen Mikhailovich Ilin (k vosmidesyatiletiyu so dnya rozhdeniya)”, Ufimsk. matem. zhurn., 4:2 (2012), 3–12  mathnet  mathscinet
    76. K. V. Emelyanov, “Raznostnaya skhema podgonki dlya singulyarno vozmuschennoi zadachi s tochkoi povorota”, Tr. IMM UrO RAN, 18, no. 2, 2012, 80–91  mathnet  elib
    77. G. P. Panasenko, “Partial asymptotic decomposition of the domain for the diffusion–discrete absorption”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 118–125  mathnet  crossref  isi  elib
    78. G. I. Shishkin, “Obuslovlennost raznostnoi skhemy metoda dekompozitsii resheniya dlya singulyarno vozmuschennogo uravneniya konvektsii-diffuzii”, Tr. IMM UrO RAN, 18, no. 2, 2012, 291–304  mathnet  elib
    79. A. I. Zadorin, S. V. Tikhovskaya, “Solution of second order nonlinear singular perturbation ordinary differential equation based on the Samarskii scheme”, Num. Anal. Appl., 6:1 (2013), 9–23  mathnet  crossref  mathscinet  elib
    80. A. I. Zadorin, S. V. Tikhovskaya, “Dvukhsetochnyi metod dlya nelineinoi singulyarno vozmuschennoi kraevoi zadachi na setke Shishkina”, Sib. zhurn. industr. matem., 16:1 (2013), 42–55  mathnet  mathscinet
    81. G. I. Shishkin, “Conditioning and stability of finite difference schemes on uniform meshes for a singularly perturbed parabolic convection-diffusion equation”, Comput. Math. Math. Phys., 53:4 (2013), 431–454  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    82. K. V. Emelyanov, “O raznostnoi skheme pervogo poryadka tochnosti dlya singulyarno vozmuschennoi zadachi s tochkoi povorota”, Tr. IMM UrO RAN, 19, no. 3, 2013, 120–135  mathnet  mathscinet  elib
    83. Sharma K.K., Rai P., Patidar K.C., “A Review on Singularly Perturbed Differential Equations with Turning Points and Interior Layers”, Appl. Math. Comput., 219:22 (2013), 10575–10609  crossref  isi
    84. L. A. Kalyakin, “Phantom asymptotic solutions”, Ufa Math. J., 6:2 (2014), 44–65  mathnet  crossref  elib
    85. A. V. Shilkov, “Even-odd parity transport equations. 2: The exact characteristic scheme for one-dimensional problems”, Math. Models Comput. Simul., 7:1 (2015), 36–50  mathnet  crossref
    86. A. V. Shilkov, “Even- and odd-parity kinetic equations of particle transport. 3: Finite analytic scheme on tetrahedra”, Math. Models Comput. Simul., 7:5 (2015), 409–429  mathnet  crossref  elib
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    89. A. I. Zadorin, “Interpolyatsiya funktsii dvukh peremennykh s bolshimi gradientami v pogranichnykh sloyakh”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2015, 55–67  mathnet  elib
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    92. I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “About the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer”, Num. Anal. Appl., 10:2 (2017), 108–119  mathnet  crossref  crossref  isi  elib
    93. A. V. Shilkov, “Reshenie ellipticheskikh uravnenii metodom luchevykh peremennykh”, Preprinty IPM im. M. V. Keldysha, 2017, 119, 36 pp.  mathnet  crossref
    94. S. F. Dolbeeva, V. N. Pavlenko, S. V. Matveev, O. N. Dementev, A. V. Melnikov, E. A. Sbrodova, A. A. Solovev, V. I. Ukhobotov, V. E. Fedorov, E. A. Fominykh, A. A. Ershov, “Arlen Mikhailovich Ilin. 85 let so dnya rozhdeniya”, Chelyab. fiz.-matem. zhurn., 2:1 (2017), 5–9  mathnet  elib
    95. I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “On the parameter-uniform convergence of exponential spline interpolation in the presence of a boundary layer”, Comput. Math. Math. Phys., 58:3 (2018), 348–363  mathnet  crossref  crossref  isi  elib
    96. Quantum Electron., 48:11 (2018), 1076–1082  mathnet  crossref  isi  elib
    97. A. V. Shilkov, “O reshenii lineinykh ellipticheskikh uravnenii vtorogo poryadka”, Matem. modelirovanie, 31:6 (2019), 55–81  mathnet  crossref  elib
    98. I. V. Popov, “O monotonnykh raznostnykh skhemakh”, Matem. modelirovanie, 31:8 (2019), 21–43  mathnet  crossref  elib
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