TEACHING

1.      Analysis

Lectures notes for second-year students of the Faculty of Electricity, Electronics and Automatics
1.    Laplace tramsform and applications to ODEs and PDEs.
2.    Complex analysis
3.    Basic numerical methods
4.    Probability and statistics
The exhibition is very closed to the content and character of mathematics in the books:
1.    E:Kreyszig, Advanced engeneering mathematics, seventh edition, 1993, John Wiley and Sons, Inc.
2.    J.L.Shiff, The Laplace transform, (1991), Springer

2.      Numerical Methods
a) Lectures notes for third-year students of Mathematics and Informatics. Faculty of Science and Education
b) Lecture Notes:
The Finite Element Method 1. Stationary Problems. 2. Evolution Problems (In Bulgarian)
3.      Theory of probability and statistics

Lectures for third-year students of speciality Mathematics and Informatics and Informatics, Faculty of Science and Education
Lecture Notes:
Theory and applications of probability and statistics. (in Bulgarian)
RESEARCH
In Editorial Board of the international journals: 
International Journal of Numerical Analysis and Modeling;
Pacific-Asian Journal of Mathematics
 Scientific interests:

1.    Numerical methods for PDEs: problems with interfaces and boundary layers.
2.    Analytical analysis of PDEs problems with interfaces and boundary layers
3.    Numerical analysis of blowing up solutions to nonlinear PDEs (especially, boundary and interface blow up)

 PUBLICATIONS (1999 - )

  Journal publications:

 1. L.G. Vulkov, Conservation laws and symmetrization of the equations of incompressible inviscid fluids, Quart. of Appl. Math., 57, N 3 (1999), pp. 549-560
 2. I. A. Braianov and L.G. Vulkov, Grid approximation for the solution of the singularly perturbed heat equation with concentrated capacity, J. of Math. Anal. Appls, v.237, 672-697 (1999)
 3. Braianov, I.A.; Vulkov L.G.: Homogeneous difference schemes for the heat equation with concentrated capacity. Comp. Math. Math. Phys. , 39 (1999), 254-261
 4. Braianov, I.; Vulkov, L.: Uniform in a small parameter convergence of Samarskii's monotone scheme and its modification for the convection-diffusion equation with concentrated source, Comp. Math. and Phys., v.40, N4, (2000), pp. 534-550
 5. L.G.Vulkov, J.D. Kandilarov, Construction and implementation of finite- difference schemes for systems of diffusion equations with localized chemical reactions, Comp. Math. and Math. Phys., V 40, N5, 2000, 705-717
 6. L.G. Vulkov, On the conservation laws in magnetohydrodynamics,  Applicable Analysis. Vol. 75(1-2), (2000), pp. 1-18
 7. Jovanovic, B.; Vulkov, L.: On the convergence of finite difference schemes for the heat equation with concentrated capacity. Numerishe Mathematik, vol.89, N.4 (2001), pp. 715-734
8. B.S. Jovanovic and L. G. Vulkov, On the convergence of difference schemes for hyperbolic problems with concentrated  data, SIAM J. Numer. Anal, 41, N 2, (2003),516-538
9. B.S. Jovanovic, L.G. Vulkov, On the rate of convergence of difference schemes for the Poisson equation with dynamical interface condition, Comp. Mеth. in Appl. Math., 3, N 1, (2003)
10. J.D.Kandilarov, L.G.Vulkov, Analysis of immerced interface difference schemes for reaction-diffusion problems with singular own sources, Comp. Meth. In Appl. Math. 3, N 2, (2003)
11. I.A.Braianov, L.G.Vulkov, Numerical Solution of Reaction-Diffusion Elliptic Interface Problem with Strong Anisontropy, Computing, 71, N 2, (2003), 153-173
12. J.D. Kandilarov, L.G.Vulkov, The immersed interface method for a nonlinear chemical diffuzion equation with local sites of reactions, Numerical Algorithms, v. 36, N4, (2004), 285-307
13. I.Tr.Angelova, L.G.Vulkov, Singularly perturbed differential equations with discontinuous coefficients and concentrated factors, Appl. Math. and Comput., v.158,  (2004), 683-701
14. B.S. Jovanovic, L.G. Vulkov, Stability of difference scheme for parabolic equations with dynamical boundary and conjugation conditions, Appl. Math. and Comput, v.163,  (2005), 849-868
15. L.G. Vulkov, B.S. Jovanovic,  Convergence of difference schemes for Poisson equations with dynamical boundary conditions, Comp. Math. and Math. Phys. v 45, N2 (2005), 287-297
16. B.S. Jovanovic, L.G. Vulkov, Energy stability for a class of parabolic interface problems, J. of Math. Anal. Appl., v.311 (2005), 120-138
17. М.N. Koleva, L.G.Vulkov, On the blow-up of finite difference solutions to the heat-difusion equation with semilinear dynamical boundary conditions Appl. Math. and Comput , v.161, (2005)
18. I.Tr.Angelova, L.G.Vulkov, High-order difference schemes for one-dimensional interface problems based on new Marchuk integral identities, J. Numer. Math. V.13, N1, (2005), 824-843
19. M. Koleva, L.Vulkov, Blow-up of continuous and semidiscrete solutions to elliptic equations with semilinear dynamical boundary conditions of parabolic type, J. Comp. Appl. Math., v. 202, N2 (2007)
20. M. Koleva, L.Vulkov, Numerical solution of the heat equation with nonlinear boundary condition in unbounded domains, Numer. Methods for PDEs , v. 23, N2 (2007)
21. J.D.Kandilarov, L.G.Vulkov, The immersed interface method for two-dimensional heat-diffusion equations with singular own sources, Appl. Numer. Math. v.57 (5-7) (2007)
22. I. Angelova, L. Vulkov, High-order difference schemes for elliptic problems with intersecting interfaces, Appl. Math. And Comp., 187 (2007) 824-843
23. I. Angelova, L. Vulkov, Marchuk identity-type second order difference schemes of 2-D and 3-D elliptic problems with intersected interfaces, Krag, J, Math., 30 (2007) 277-292
24. B.S. Jovanovic, L.G. Vulkov, On the convergence of difference scheme for parabolic problems with concentrated data, Int. J. Numer. Anal. and Modeling, v.5, N3, (2008), 386-407
25. B.S.Jovanovic, L.G.Vulkov, Finite difference approximations for some interface problems with variable coefficients Appl. Numer. Math. (accepted)
26. B.S. Jovanovic, L.G. Vulkov, Finite difference approximations of strong solutions of a parabolic interface  problem on disconnected domains, Publ. Inst. Math. (2008) (accepted)
27. L.G.Vulkov, Blow-up of some quasilinear equations with dynamical boundary conditions, Appl.  Math. Comp, v.191 (2007)
28. B.S. Jovanovic, L.G. Vulkov,  Formulation and analysis of parabolic interface problems on disjoint intervals (submitted)
29. B.S. Jovanovic, L.G. Vulkov, Numerical solution of a parabolic transmission problem on disjoint intervals (submitted)
30. B.S. Jovanovic and L.G. Vulkov, Analysis of semidiscrete approximations of blow up weak solutions to semilinear parabolic equations, (submitted)
31. B.S. Jovanovic and L.G. Vulkov, Richardson extrapolation in spectral problems with eigenvalues in boundary and conjugation conditions (submitted)
32. J. D. Kandilarov, L.G.Vulkov, Construction and analysis of immersed interface difference schemes for  reaction-diffusion equations with moving own concentrated sources (submitted)
33. B.S. Jovanovic and L.G. Vulkov, Regularity of solutions and a priori estimates for elliptic interface problems  (submitted)

Conference publications:

 1. L.G. Vulkov, An ADI Method for Singularly Perturbed Nonstationary Problems with Curvlinear Boundary or Interface, pp.96-98 Appls of Math. in Engeneering and Economics, Proceed. of the XXV Summer School, Sozopol'99 Eds. B.I. Cheshankov, M.D. Todorov, Heron Press, Sofia, (2000)
 2. I.A. Braianov, L.G. Vulkov, Uniformly convergent difference scheme for the singularly perturbed convection-diffusion parabolic problem with concentrated capacity, NOVA Science Publishers, Inc., New York, (2000), 1-169
 3. I.A. Braianov, J.D. Kandilarov, L.G. Vulkov, Numerical solution of diffusion-desorbtion problems with small diffusion coefficients and localized chemical reactions, Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems, NOVA Science Publishers, Inc., New York, (2000), pp. 169-177
 4. B.S.Jovanovic, L.G. Vulkov, On the convergence of difference scheme for the string equation with concentrated mass. FDS-2000 Conference, pp. 107-116. B. Ciegis et al. (Eds).
 5. J.D. Kandilarov, L.G.Vulkov, A.I. Zadorin, A method of lines approach to the numerical solution of singularly perturbed elliptic problems, Lect. Notes in Comp. Sci , v 1988, (2001), pp. 451-459
 6. Jovanovic, B.S.; Vulkov, L.G. Operator's approach to the problems with concentrated factors. Lect. Notes in Comput. Sci., v. 1988, (2001), pp. 439-451
 7. Jovanovic, B.S.; Kandilarov, J.D.; Vulkov, L.G.: Construction and convergence of difference scheme for a model elliptic equation with Dirac--delta function coefficient. Lect. Notes Comput. Sci., v. 1988, (2001), pp. 431-439
8. B. Jovanovic, L. Vulkov, Stability and convergence of difference schemes for parabolic interface problems, FILOMAT, v.15 (2002), pp.235-244
9. I.Tr. Dimitrova, L.G. Vulkov, On the numerical solution of singularly perturbed interface problems, pp.249-257, Appls of Math. in Engeneering and Economics, Proceed. of the XXV Summer School, Sozopol'99 Eds. D. Ivanchev, M.D. Todorov, Heron Press, Sofia, (2002)
10. I.Tr. Dimitrova, L.G. Vulkov, High order uniform methods for singularly perturbed reaction-diffusion problems with discontinuous coefficients and singular sources, FILOMAT, v.15 (2002)
11. I.A. Braianov, L.G. Vulkov, Uniformly convergent finite-volume difference scheme for singularly perturbed convection-diffusion interface problems, Lect. Notes Comput. Sci (2003)
12. B.S.Jovanovic, L.G.Vulkov, Finite difference approximations of an elliptic interface problem with variable coefficients, Lect. Notes in Comp.Sci. v.3401 (2005)
13. I. Angelova, L. Vulkov, Uniformly convergent of finite-difference schemes for a reaction-diffusion interface problems, Lect. Notes Comp. Sci. (2007)
14. J. Kandilarov, M. Koleva and L. Vulkov, A second-order Cartesian grid finite volume technique for elliptic interface problems, Lect. Notes Comp. Sci, v.4818 (2007)
15. L.G. Vulkov, Well posedness and a monotone iterative method for a nonlinear interface problem on disjoint intervals, Amer. Inst. Of Physics, Proceedings Series 946 (2007)
16. M. Koleva, L.Vulkov, Blow-Up of Finite Difference Solutions to Parabolic Equations with Semilinear Dynamical Boundary Conditions, Proceedings of Fourth International Conference “Finite Difference Methods: Theory and Applications, I. Farago, P. vabishchevich and L. Vulkov (Eds), 2007, 239-245
17. M. Koleva, L. G. Vulkov, Blow-up of finite difference solutions to parabolic equations with semilinear dynamical boundary conditions, Proceedings of Fourth International Conference “Finite Difference Methods: Theory and Applications, I. Farago, P. vabishchevich and L. Vulkov (Eds), 2007, 239-245

 Conference Proceedings Books:

 1. L.G. Vulkov, J.J.H.Miller and G.I. Shishkin (Eds.), Analytical  and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems, Nova Science Publishers, New York, 2000.
 2. L.Vulkov, J. Wasniewski, P. Yalamov (Eds), Numerical Analysis and Its Applications, Lect. Notes in Comp. Sci., v. 1988 (2001)
3. Z.Li, L. Vulkov and J.Wasniewski (Eds), Numerical Analysis and its Applications, Lecture Notes on Computer Sci. v 3401 (2005)
4. I. Farago, P. Vabishchevich and L. Vulkov (Editors), Finite Difference Methods: Theory and Applications, Proceedings of Fourth International Conference FDM: T & A’06, August 26-29, 2006, Ruse University (2007)

 Doctoral Degree Students:

1. I.N. Panajotova - defended, 2000;
2. I.A. Braianov, defended, 2003;
3. I.D. Kandilarov, defended, 2005;
4. M. Koleva, defended, 2007;
5. I.Tr.Angelova, defended, 2008
6. I.R. Georgiev, doctorant