52 citations · 535 across the 39 of their papers we have counts for
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Generalized exponential basis for efficient solving of homogeneous diffusion free boundary problems: Russian option pricing
Igor V. Kravchenko, Vladislav V. Kravchenko, Sergii M. Torba +1
This paper develops a method for solving free boundary problems for time-homogeneous diffusions. We combine the complete exponential system of solutions for the heat equation, tran…
Analytic approximation of solutions of parabolic partial differential equations with variable coefficients
Vladislav V. Kravchenko, Josafath A. Otero, Sergii M. Torba
A complete family of solutions for the one-dimensional reaction-diffusion equation \[ u_{xx}(x,t)-q(x)u(x,t) = u_t(x,t) \] with a coefficient depending on is constructed. T…
Solution of parabolic free boundary problems using transmuted heat polynomials
Igor V. Kravchenko, Vladislav V. Kravchenko, Sergii M. Torba
A numerical method for free boundary problems for the equation \[ u_{xx}-q(x)u=u_t \] is proposed. The method is based on recent results from transmutation operators theory allowin…
Modulated electromagnetic fields in inhomogeneous media, hyperbolic pseudoanalytic functions and transmutations
Kira V. Khmelnytskaya, Vladislav V. Kravchenko, Sergii M. Torba
The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bico…
Wave polynomials, transmutations and Cauchy's problem for the Klein-Gordon equation
Kira V. Khmelnytskaya, Vladislav V. Kravchenko, Sergii M. Torba +1
We prove a completeness result for a class of polynomial solutions of the wave equation called wave polynomials and construct generalized wave polynomials, solutions of the Klein-G…
Construction of transmutation operators and hyperbolic pseudoanalytic functions
Vladislav V. Kravchenko, Sergii M. Torba
A representation for integral kernels of Delsarte transmutation operators is obtained in the form of a functional series with the exact formulas for the terms of the series. It is…