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# Laboratory of Difference Methods

Head of the laboratory: Nikolaev Evgeny, Leading Research Fellow, PhD

The Laboratory of Difference Methods was founded by A.A.Samarsky, Academician of RAS, in the middle of the 60s. For more than 50 years the Laboratory’s theoretical research has been focused on numerical methods for problems described by systems of partial differential equations. Methods and algorithms developed by the scientific researchers have been implemented in a general-purpose program library and problem-oriented packages. They are used for numerical simulation in microelectronics, magnetic hydrodynamics, magnetic gas dynamics, supersonic plasma aerodynamics and for solving elasticity theory problems.

### Staff members:

- Ardelyan Nikolay, Leading Research Fellow, Dr.Sc.
- Belukhina Inna, Senior Research Fellow, PhD
- Kosmachevsky Konstantin, Senior Research Fellow, PhD
- Ershova Tatiana, Research Fellow, PhD
- Anpilov Sergey, Researcher, PhD
- Sablin Mark, Researcher, PhD
- Zolotareva Natalia, Researcher, PhD
- Laponin Vladislav, Researcher
- Yasminova Olga, Leading Mathematician
- Galochkina Elena, Mathematician
- Glukhova Marina, Mathematician

### Regular courses:

Methods for solving grid equations by Leading Research Fellow Nikolaev, 32 lecture hours, 5th and 6th semesters.

## Main Scientific directions

Current directions of the laboratory’s scientific research are aimed at creating and applying numerical methods for solving partial differential equations, iterative methods for solving sparse systems of linear equations and adaptive grid methods for solving singularly perturbation ODE and PDE problems.

### References:

- N.V.Ardelyan, K.V.Kosmachevskii and V.L.Bychkov, Features of combined plasmas // IEEE Trans. on Plasma Science, vol. 36, no. 6, pp. 2892-2897, 2008.
- N.V.Ardelyan, V.L.Bychkov, I.V.Kochetov and K.V.Kosmachevskii, Non-self-maintained discharge plasma in propane-air mixture // IEEE Trans. on Plasma Science, vol. 39. no. 12, part 1, pp. 3323-3330, 2011.
- T.Ya.Ershova, Solution of the Dirichlet problem for a singularly perturbed reaction-diffusion equation in a square on a Bakhvalov grid // Moscow University Computational Mathematics and Cybernatics, vol. 33, no. 4, pp. 171-180, 2009.
- E.S.Nikolaev and O.V Shishkina, A method of solving the Dirichlet problem for the second-order elliptic equation in a polygonal domain on an adaptively refined mesh sequence // Moscow University Computational Mathematics and Cybernetics, vol. 29, no. 4, pp. 1-14, 2005.
- N.D.Zolotareva and E.S. Nikolaev, Method for constructing meshes adapting to the solution of boundary value problems for ordinary differential equations of the second and fourth orders // Differential Equations, vol. 45, no. 8, pp. 1189-1202, 2009.
- N.V.Ardelyan, D.V.Bychkov, V.L.Bychkov, V.A.Gudovich, S.V.Denisiuk, I.V.Kochetov and K.V.Kosmachevskii, Non-self maintained gas discharge for plasma impact on gas flammable mixtures // Proc. 48-th AIAA Aerospace Science Meeting and Exhibition. N AIAA-2010-0269. Orlando, USA: Amer. Phys. Soc., pp. 1-12, 2010.
- N.V.Ardelyan, D.V.Bychkov, I.V.Kochetov and K.V.Kosmachevskii, Non-self-maintained discharge and electron beam plasma in propane-air mixture. I. Theoretical results // Proc. 6-th Intern. Workshop and Exhibition on Plasma Assisted Combustion (IWEPAC). Lampoldshauzen, Germany: Institute of Space Propulsion, German Aerospace Centre, pp. 58-60, 2010.
- N.V.Ardelyan, D.V.Bychkov, I.V.Kochetov and K.V.Kosmachevskii, On pulsed discharge in humid air // Proc. 48-th AIAA Aerospace Science Meeting and Exhibition. N AIAA-2010-1589. Orlando, USA: Amer. Phys. Soc., pp. 1-10, 2010.
- S.G.Moiseenko, G.S.Bisnovatyi-Kogan and N.V. Ardelyan, Magnetorotational processes in core collapse supernovae // Astrophysics and Cosmology after Gamow. AIP Conference Proceedings. Berlin, Germany: Springer, no. 1206, pp. 282-292, 2010. 10.D.V.Bychkov, N.V. Ardelyan, K.V.Kosmachevskii and I.V.Kochetov, Non-self maintained gas discharge for plasma impact on flammable gases (theory) // Proc. 49-th AIAA Aerospace Science Meeting and Exhibition. N AIAA-2011-1215. Orlando, USA: Amer. Phys. Soc., 2011.

### Recent publications:

• 2013

- Ardelyan N.V., Bychkov V.L., Kochetov I.V., Kosmachevskii K.V. Kinetic model of pulsed discharge in humid air // IEEE Trans. on Plasma Science. 2013. 41. N 12. P. 1-1.
- Zolotareva N.D., Nikolaev E.S. Adaptive p-version of the finite element method for solving boundary value problems for ordinary second-order differential equations // Differential Equations. 2013. 49. N 7. P. 835-848.
- Ardelyan N.V., Bychkov V.L., Bychkov D.V., Kosmachevskii K.V. Electron-beam and non-self-maintained driven plasmas for PAC // Plasma assisted combustion, gasification, and pollution control. N 1. Denver, USA: Outskirts Press, Inc., 2013. P. 106-304.

• 2012

- Ardelyan N.V., Bychkov V.L., Bychkov D.V., Denisiuk S.V., Kosmachevskii K.V. Non selfmaintained gas discharge for flammable gases impact // Химическая физика. 2012. 31. N 2. P. 48-60.
- Ardelyan N.V., Bychkov V.L., Bychkov D.V., Denisiuk S.V., Kosmachevskii K.V. Non-selfmaintained gas discharge for flammable gases impact // Russ. J. Phys. Chem. B. 2012. 6. N 1. P. 128-139.
- Ardelyan N.V., Bychkov V.L., Kosmachevskii K.V. Plasma jet ignition of a propane-air stoichiometric mixture (cylindrical jet) // IEEE Trans. on Plasma Science. 2012. 40. N 12. P. 1-1.
- Ardelyan N.V., Bychkov V.L., Kosmachevskii K.V. Plasma jet ignition of a propane-air stoichiometric mixture (flat jet) // IEEE Trans. on Plasma Science. 2012. 40. N 12. P. 1-1.
- Ershova T.Ya. A mixed boundary value problem for a singularly perturbed reaction-diffusion equation in an L-shaped domain // Moscow University Comput. Mathematics and Cybern. 2012. 36. N 3. P. 109-119.