Borisov, D. I.
Published in
Computational Mathematics and Mathematical Physics

A singularly perturbed eigenvalue problem for the Laplacian in a cylinder is considered. The problem is characterized by frequent nonperiodic alternation of boundary conditions imposed on narrow strips lying on the cylinder’s lateral surface. The width of the strips is an arbitrary function of a small parameter and can oscillate rapidly, with the n...

Kerimov, M. K.
Published in
Computational Mathematics and Mathematical Physics

Tereshin, E. B. Trofimov, V. A. Fedotov, M. V.
Published in
Computational Mathematics and Mathematical Physics

Conservative finite-difference schemes are constructed for the problems of self-action of a femtosecond laser pulse and of second-harmonic generation in a one-dimensional nonlinear photonic crystal with nonreflecting boundary conditions. The invariants of the governing equations are found taking into account these conditions. Nonreflecting conditio...

Amirat, Y. Chechkin, G. A. Gadyl’shin, R. R.
Published in
Computational Mathematics and Mathematical Physics

The asymptotic behavior of solutions to spectral problems for the Laplace operator in a domain with a rapidly oscillating boundary is analyzed. The leading terms of the asymptotic expansions for eigenelements are constructed, and the asymptotics are substantiated for simple eigenvalues.

Botashev, Kh. I.
Published in
Computational Mathematics and Mathematical Physics

Theorems on the localization of exact solutions are proved for a quasilinear mathematical model describing quasi-periodic processes. Based on these theorems, constructive algorithms are proposed for calculating quasi-periodic solutions with guaranteed accuracy. Quasi-periodic motions play an important role in engineering and physics, where they oft...

Pinchukov, V. I.
Published in
Computational Mathematics and Mathematical Physics

Two types of implicit fourth-order Runge-Kutta schemes are constructed for first-order ordinary differential equations, multidimensional transfer equations, and compressible gas equations. The absolute stability of the schemes is proved by applying the principle of frozen coefficients. Adaptive artificial viscosity ensuring good time convergence an...

Kerimov, M. K.
Published in
Computational Mathematics and Mathematical Physics

Kornev, A. A.
Published in
Computational Mathematics and Mathematical Physics

Let S be an operator in a Banach space H and Si(u) (i = 0, 1, ..., u ∈ H) be the evolutionary process specified by S. The following problem is considered: for a given point z0 and a given initial condition a0, find a correction l such that the trajectory {Si(a0 + l)} approaches }Si(z0)} for 0

Kel’manov, A. V. Mikhailova, L. V.
Published in
Computational Mathematics and Mathematical Physics

The problem of joint a posteriori detection of reference fragments in a quasi-periodic sequence and its partition into segments containing series of recurring fragments from the reference tuple is solved. It is assumed that (i) an ordered reference tuple of sequences to be detected is given, (ii) the number of desired fragments is known, (iii) the ...

Shishkin, G. I.
Published in
Computational Mathematics and Mathematical Physics

A boundary value problem for a singularly perturbed parabolic convection-diffusion equation on an interval is considered. The higher order derivative in the equation is multiplied by a parameter ɛ that can take arbitrary values in the half-open interval (0, 1]. The first derivative of the initial function has a discontinuity of the first kind at th...