## Found 198 Documents (Results 1–100)

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### Asymptotics of the solution of the first boundary value problem for a singularly perturbed differential equation in partial derivatives of the second order of parabolic type. (Russian. English summary)Zbl 07503628

MSC:  35B25 35C20 35K20
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### A singularly perturbed system of parabolic equations. (English)Zbl 07503351

MSC:  35B25 35K51
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### Development of methods of asymptotic analysis of transition layers in reaction-diffusion-advection equations: theory and applications. (English. Russian original)Zbl 1481.35009

Comput. Math. Math. Phys. 61, No. 12, 2068-2087 (2021); translation from Zh. Vychisl. Mat. Mat. Fiz. 61, No. 12, 2074-2094 (2021).
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### On unstable solutions with a nonmonotone boundary layer in a two-dimensional reaction-diffusion problem. (English. Russian original)Zbl 1481.35028

Math. Notes 110, No. 6, 922-931 (2021); translation from Mat. Zametki 110, No. 6, 899-910 (2021).
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### Robust numerical method for singularly perturbed semilinear parabolic differential difference equations. (English)Zbl 07429016

MSC:  65-XX 35-XX
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### A high order robust numerical scheme for the generalized Stein’s model of neuronal variability. (English)Zbl 07409802

MSC:  65L11 65M12 35K20
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### Corner boundary layer in boundary value problems for singularly perturbed parabolic equations with cubic nonlinearities. (English. Russian original)Zbl 1461.35019

Comput. Math. Math. Phys. 61, No. 2, 242-253 (2021); translation from Zh. Vychisl. Mat. Mat. Fiz. 61, No. 2, 256-267 (2021).
MSC:  35B25 35K20 35K58
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### Asymptotic solution of coefficient inverse problems for Burgers-type equations. (English. Russian original)Zbl 1450.35293

Comput. Math. Math. Phys. 60, No. 6, 950-959 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 6, 975-984 (2020).
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### An adaptive mesh selection strategy for solving singularly perturbed parabolic partial differential equations with a small delay. (English)Zbl 1465.65074

Kumar, B. Rushi (ed.) et al., Applied mathematics and scientific computing. International conference on advances in mathematical sciences, ICAMS, Vellore, India, December 1–3, 2017. Volume II. Selected papers. Cham: Birkhäuser. Trends Math., 67-76 (2019).
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### Existence and asymptotic stability of periodic two-dimensional contrast structures in the problem with weak linear advection. (English. Russian original)Zbl 1435.35033

Math. Notes 106, No. 5, 771-783 (2019); translation from Mat. Zametki 106, No. 5, 708-722 (2019).
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### Numerical solution of singularly perturbed parabolic problems by a local kernel-based method with an adaptive algorithm. (English)Zbl 1449.35034

MSC:  35B25 65M99
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### Ordinary differential equations with power boundary layers. (English. Ukrainian original)Zbl 1431.34074

J. Math. Sci., New York 242, No. 3, 427-431 (2019); translation from Ukr. Mat. Visn. 15, No. 4, 536-542 (2018).
MSC:  34E15 34A12
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### Improved computer scheme for a singularly perturbed parabolic convection-diffusion equation. (English)Zbl 1434.65134

Dimov, Ivan (ed.) et al., Finite difference methods. Theory and applications. 7th international conference, FDM 2018, Lozenetz, Bulgaria, June 11–16, 2018. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 11386, 80-91 (2019).
MSC:  65M06 65M22 65M12
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### $$\varepsilon$$-uniform numerical technique for the class of time dependent singularly perturbed parabolic problems with state dependent retarded argument arising from generalised Stein’s model of neuronal variability. (English)Zbl 1412.65056

MSC:  65L11 65M12 35K20
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### A higher order uniformly convergent method for singularly perturbed delay parabolic partial differential equations. (English)Zbl 1398.65185

MSC:  65L11 65M06 65M12
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### Asymptotic-numerical method for the location and dynamics of internal layers in singular perturbed parabolic problems. (English)Zbl 1368.65167

Dimov, Ivan (ed.) et al., Numerical analysis and its applications. 6th international conference, NAA 2016, Lozenetz, Bulgaria, June 15–22, 2016. Revised selected papers. Cham: Springer (ISBN 978-3-319-57098-3/pbk; 978-3-319-57099-0/ebook). Lecture Notes in Computer Science 10187, 721-729 (2017).
MSC:  65M22 35K57 35B25
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### A singularly perturbed boundary value problems with fractional powers of elliptic operators. (English)Zbl 1368.65210

Dimov, Ivan (ed.) et al., Numerical analysis and its applications. 6th international conference, NAA 2016, Lozenetz, Bulgaria, June 15–22, 2016. Revised selected papers. Cham: Springer (ISBN 978-3-319-57098-3/pbk; 978-3-319-57099-0/ebook). Lecture Notes in Computer Science 10187, 141-152 (2017).
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### Use of asymptotics for new dynamic adapted mesh construction for periodic solutions with an interior layer of reaction-diffusion-advection equations. (English)Zbl 1368.65166

Dimov, Ivan (ed.) et al., Numerical analysis and its applications. 6th international conference, NAA 2016, Lozenetz, Bulgaria, June 15–22, 2016. Revised selected papers. Cham: Springer (ISBN 978-3-319-57098-3/pbk; 978-3-319-57099-0/ebook). Lecture Notes in Computer Science 10187, 107-118 (2017).
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### Numerical method for a singularly perturbed boundary value problem for a linear parabolic second order delay differential equation. (English)Zbl 1453.65184

Valarmathi, Sigamani (ed.) et al., Differential equations and numerical analysis, DEANA. Selected papers based on the presentations at the workshop, Tiruchirappalli, India, January 5–7, 2015. New Delhi: Springer. Springer Proc. Math. Stat. 172, 117-133 (2016).
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### The initial-boundary value problem for a singularly perturbed parabolic equation in the case of double and triple root of the degenerate equation. (Russian. English summary)Zbl 1441.35149

MSC:  35K91 35B25 35K20
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### Difference scheme for a singularly perturbed parabolic convection-diffusion equation in the presence of perturbations. (English. Russian original)Zbl 1336.65142

Comput. Math. Math. Phys. 55, No. 11, 1842-1856 (2015); translation from Zh. Vychisl. Mat. Mat. Fiz. 55, No. 11, 1876-1892 (2015).
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### Convergence of three-step Taylor Galerkin finite element scheme based monotone Schwarz iterative method for singularly perturbed differential-difference equation. (English)Zbl 1326.65132

MSC:  65M60 65M12 35K20
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### Asymptotic-numerical method for moving fronts in two-dimensional R-D-A problems. (English)Zbl 1359.65231

Dimov, Ivan (ed.) et al., Finite difference methods, theory and applications. 6th international conference, FDM 2014, Lozenetz, Bulgaria, June 18–23, 2014. Revised selected papers. Cham: Springer (ISBN 978-3-319-20238-9/pbk; 978-3-319-20239-6/ebook). Lecture Notes in Computer Science 9045, 408-416 (2015).
MSC:  65M99 35K57 35B25
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### A higher order accurate solution decomposition scheme for a singularly perturbed parabolic reaction-diffusion equation. (English. Russian original)Zbl 1318.65056

Comput. Math. Math. Phys. 55, No. 3, 386-409 (2015); translation from Zh. Vychisl. Mat. Mat. Fiz. 55, No. 3, 393-416 (2015).
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### Robust numerical scheme for singularly perturbed convection-diffusion parabolic initial-boundary-value problems on equidistributed grids. (English)Zbl 1352.65292

MSC:  65M12 65M06 35K20
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### Asymptotics of the front motion in the reaction-diffusion-advection problem. (English. Russian original)Zbl 1327.35174

Comput. Math. Math. Phys. 54, No. 10, 1536-1549 (2014); translation from Zh. Vychisl. Mat. Mat. Fiz. 54, No. 10, 1594-1607 (2014).
MSC:  35K57 35B25 35C20
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### Computer difference scheme for a singularly perturbed convection-diffusion equation. (Russian, English)Zbl 1313.35173

Zh. Vychisl. Mat. Mat. Fiz. 54, No. 8, 1256-1269 (2014); translation in Comput. Math. Math. Phys. 54, No. 8, 1221-1233 (2014).
MSC:  35K57 35K67
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### On a singularly perturbed mixed problem for a linear parabolic equation with nonlinear boundary conditions. (Russian, English)Zbl 1313.35190

Zh. Vychisl. Mat. Mat. Fiz. 54, No. 1, 80-88 (2014); translation in Comput. Math. Math. Phys. 54, No. 1, 74-82 (2014).
MSC:  35K60
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### Existence and asymptotic stability of periodic solutions with an interior layer of reaction-advection-diffusion equations. (English)Zbl 1325.35099

MSC:  35K57 35K20
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### Conditioning and stability of finite difference schemes on uniform meshes for a singularly perturbed parabolic convection-diffusion equation. (Russian, English)Zbl 1299.35171

Zh. Vychisl. Mat. Mat. Fiz. 53, No. 4, 575-599 (2013); translation in Comput. Math. Math. Phys. 53, No. 4, 431-454 (2013).
MSC:  35K57
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### Asymptotic-numerical investigation of generation and motion of fronts in phase transition models. (English)Zbl 1351.35081

Dimov, Ivan (ed.) et al., Numerical analysis and its applications. 5th international conference, NAA 2012, Lozenetz, Bulgaria, June 15–20, 2012. Revised selected papers. Berlin: Springer (ISBN 978-3-642-41514-2/pbk). Lecture Notes in Computer Science 8236, 524-531 (2013).
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### Comparison principle for reaction-diffusion-advection problems with boundary and internal layers. (English)Zbl 1351.35085

Dimov, Ivan (ed.) et al., Numerical analysis and its applications. 5th international conference, NAA 2012, Lozenetz, Bulgaria, June 15–20, 2012. Revised selected papers. Berlin: Springer (ISBN 978-3-642-41514-2/pbk). Lecture Notes in Computer Science 8236, 62-72 (2013).
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### Contrast structures in the reaction-diffusion-advection equations in the case of balanced advection. (Russian, English)Zbl 1274.35190

Zh. Vychisl. Mat. Mat. Fiz. 53, No. 3, 365-376 (2013); translation in Comput. Math. Math. Phys. 53, No. 3, 273-283 (2013).
MSC:  35K57
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### On the asymptotics of the solution to a singularly perturbed system of first-order partial differential equations with small nonlinearity in the critical case. (Russian, English)Zbl 1274.35212

Zh. Vychisl. Mat. Mat. Fiz. 52, No. 7, 1267-1276 (2012); translation in Comput. Math. Math. Phys. 52, No. 7, 1035-1043 (2012).
MSC:  35L04
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### Asymptotics of the solution to parabolic problem with the limit operator having no spectra. (Russian)Zbl 1274.35016

MSC:  35B25 35K10 35K20
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### The initial boundary value problem for a nonlocal singularly perturbed reaction-diffusion equation. (Russian, English)Zbl 1274.35193

Zh. Vychisl. Mat. Mat. Fiz. 52, No. 6, 1042-1047 (2012); translation in Comput. Math. Math. Phys. 52, No. 6, 926-931 (2012).
MSC:  35K57
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### Finite element analysis for mass-lumped three-step Taylor Galerkin method for time dependent singularly perturbed problems with exponentially fitted splines. (English)Zbl 1366.74076

MSC:  74S05 65M06 35K55
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### On the asymptotics of solution of one problem of optimal control of the small-parameter parabolic equation. (English. Russian original)Zbl 1232.49025

Autom. Remote Control 72, No. 1, 61-73 (2011); translation from Avtom. Telemekh. 2011, No. 1, 66-79 (2011).
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### On periodic solutions to singularly perturbed parabolic problems in the case of multiple roots of the degenerate equation. (Russian, English)Zbl 1224.35225

Zh. Vychisl. Mat. Mat. Fiz. 51, No. 1, 44-55 (2011); translation in Comput. Math. Math. Phys. 51, No. 1, 40-50 (2011).
MSC:  35K65 35B10 35B25
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### An efficient numerical method for a system of singularly perturbed semilinear reaction-diffusion equations. (English)Zbl 1318.65055

Dimov, Ivan (ed.) et al., Numerical methods and applications. 7th international conference, NMA 2010, Borovets, Bulgaria, August 20–24, 2010. Revised papers. Berlin: Springer (ISBN 978-3-642-18465-9/pbk). Lecture Notes in Computer Science 6046, 486-493 (2011).
MSC:  65M06 35K57 35K58
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### Front motion in the parabolic reaction-diffusion problem. (Russian, English)Zbl 1224.35197

Zh. Vychisl. Mat. Mat. Fiz. 50, No. 2, 276-285 (2010); translation in Comput. Math., Math. Phys. 50, No. 2, 264-273 (2010).
MSC:  35K57
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### Asymptotic stability via the Kreĭn-Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems. (English)Zbl 1211.35023

Reviewer: Jiaqi Mo (Wuhu)
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### The Richardson scheme for the singularly perturbed parabolic reaction-diffusion equation in the case of a discontinuous initial condition. (Russian, English)Zbl 1199.65284

Comput. Math., Math. Phys. 49, No. 8, 1348-1368 (2009); translation from Zh. Vychisl. Mat. Mat. Fiz. 49, No. 8, 1416-1436 (2009).
MSC:  65M06 35K57 35B25
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### Parameter-uniform hybrid numerical scheme for time-dependent convection-dominated initial-boundary-value problems. (English)Zbl 1185.65149

Reviewer: S. Burys (Kraków)
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### Improved difference scheme for a singularly perturbed parabolic reaction-diffusion equation with discontinuous initial condition. (English)Zbl 1233.65060

Margenov, Svetozar (ed.) et al., Numerical analysis and its applications. 4th international conference, NAA 2008, Lozenetz, Bulgaria, June 16–20, 2008. Revised selected papers. Berlin: Springer (ISBN 978-3-642-00463-6/pbk). Lecture Notes in Computer Science 5434, 116-127 (2009).
MSC:  65M06 35B25 35K57
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### Nonlocal heat flows preserving the $$L^2$$ energy. (English)Zbl 1154.35364

MSC:  35K05 35K55 49N60
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### Approximation of the solution and its derivative for the singularly perturbed Black-Scholes equation with nonsmooth initial data. (English)Zbl 1210.91134

Zh. Vychisl. Mat. Mat. Fiz. 47, No. 3, 460-480 (2007); translation in Comput. Math. Math. Phys. 47, No. 3, 442-462 (2007).
MSC:  91G20 91G80
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### Nonstationary three-dimensional contrasting structures. (Russian, English)Zbl 1210.35157

Zh. Vychisl. Mat. Mat. Fiz. 47, No. 1, 64-66 (2007); translation in Comput. Math. Math. Phys. 47, No. 1, 62-64 (2007).
MSC:  35K60
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### Singularly perturbed two-dimensional parabolic problem in the case of intersecting roots of the reduced equation. (Russian, English)Zbl 1210.35140

Zh. Vychisl. Mat. Mat. Fiz. 47, No. 4, 646-654 (2007); translation in Comput. Math. Math. Phys. 46, No. 4, 620-628 (2007).
MSC:  35K10 35B20
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### Asymptotic analysis and domain decomposition for a singularly perturbed reaction–convection–diffusion system with shock–interior layer interactions. (English)Zbl 1108.35006

Reviewer: Jiaqi Mo (Wuhu)
MSC:  35B25 35K57 35K50
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### Stationary internal layers in a reaction-advection-diffusion integro-differential system. (Russian, English)Zbl 1210.35151

Zh. Vychisl. Mat. Mat. Fiz. 46, No. 4, 624-646 (2006); translation in Comput. Math. Math. Phys. 46, No. 4, 594-615 (2006).
MSC:  35K57

### On the stability and domain of attraction of asymptotically nonsmooth stationary solutions to a singularly perturbed parabolic equation. (Russian, English)Zbl 1210.35147

Zh. Vychisl. Mat. Mat. Fiz. 46, No. 3, 433-444 (2006); translation in Comput. Math. Math. Phys. 46, No. 3, 413-424 (2006).
MSC:  35K20 35B25

### Grid approximation of singularly perturbed parabolic equations in the presence of weak and strong transient layers induced by a discontinuous right-hand side. (Russian, English)Zbl 1210.35145

Zh. Vychisl. Mat. Mat. Fiz. 46, No. 3, 407-420 (2006); translation in Comput. Math. Math. Phys. 46, No. 3, 388-401 (2006).
MSC:  35K15 35B25 65L50

### A method of asymptotic constructions with improved accuracy for quasilinear singularly perturbed parabolic convection-diffusion equation. (Russian, English)Zbl 1210.65143

Zh. Vychisl. Mat. Mat. Fiz. 46, No. 2, 242-261 (2006); translation in Comput. Math. Math. Phys. 46, No. 2, 231-250 (2006).
MSC:  65L50 35B25

### Grid approximation of singularly perturbed parabolic convection-diffusion equations subject to a piecewise smooth initial condition. (Russian, English)Zbl 1210.35148

Zh. Vychisl. Mat. Mat. Fiz. 46, No. 1, 52-76 (2006); translation in Comput. Math. Math. Phys. 46, No. 1, 49-72 (2006).
MSC:  35K20 34E15

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