arXiv subjects

Lubin G. Vulkov

Publications and source records attributed to Lubin G. Vulkov.

5 recordsLinked to original sources

arXiv2016

Numerical solution of a parabolic system in air pollution

An air pollution model is generally described by a system of PDEs on unbounded domain. Transformation of the independent variable is used to convert the problem for nonlinear air pollution on finite computational domain. We investigate the new, degenerated parabolic problem in Sobolev spaces with weights for well-posedness and positivity of the solution. Then we construct a fitted finite volume difference scheme. Some results from computations are presented.

cs.CE↗

arXiv2016

High order finite difference schemes on non-uniform meshes for the time-fractional Black-Scholes equation

We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are discussed.

q-fin.CP↗

arXiv2016

Two-grid algorithms for singularly perturbed reaction-diffusion problems on layer adapted meshes

We propose a new two-grid approach based on Bellman-Kalaba quasilinearization and Axelsson-Xu finite element two-grid method for the solution of singularly perturbed reaction-diffusion equations. The algorithms involve solving one inexpensive problem on coarse grid and solving on fine grid one linear problem obtained by quasilinearization of the differential equation about an interpolant of the computed solution on the coarse grid. Different meshes (of Bakhvalov, Shishkin and Vulanović types) are examined. All the schemes are uniformly convergent with respect to the small parameter. We show theoretically and numerically that the global error of the two-grid method is the same as of the nonlinear problem solved directly on the fine layer-adapted mesh.

cs.CE↗

arXiv2015

IMEX schemes for a Parabolic-ODE system of European Options with Liquidity Shocks

The coupled system, where one is a degenerate parabolic equation and the other has not a diffusion term arises in the modeling of European options with liquidity shocks. Two implicit-explicit (IMEX) schemes that preserve the positivity of the differential problem solution are constructed and analyzed. Numerical experiments confirm the theoretical results and illustrate the high accuracy and efficiency of the schemes in combination with Richardson extrapolation

q-fin.CP↗

arXiv2014

A Positive Flux Limited Difference Scheme for Option Pricing 2D Fully Non-linear Parabolic Equation with Uncertain Correlation

We consider a two-asset non-linear model of option pricing in an environment where the correlation is not known precisely, but varies between two known values. First we discuss the non-negativity of the solution of the equation. Next, we construct and analyze a positivity preserving, flux-limited difference scheme for the corresponding boundary value problem. Numerical experiments are analyzed.

math.NA↗