Yuri M. Dimitrov

collaborators

5 papers

math.NA2018

Asymptotic expansions and approximations for the Caputo derivative

Yuri Dimitrov, Radan Miryanov, Venelin Todorov

In this paper we use the asymptotic expansions of the binomial coefficients and the weights of the L1 approximation to obtain approximations of order $2 - α$ and second-order approxi…

math.NA2018

Numerical solutions of ordinary fractional differential equations with singularities

Yuri Dimitrov, Ivan Dimov, Venelin Todorov

The solutions of fractional differential equations (FDEs) have a natural singularity at the initial point. The accuracy of their numerical solutions is lower than the accuracy of t…

math.NA2016

Approximations for the Caputo Derivative (I)

Yuri Dimitrov

In this paper we construct approximations for the Caputo derivative of order $1 - α, 2 - α, 2$ and $3 - α$ . The approximations have weights $0.5 ((k + 1)^{- α} - (k - 1)^{- α}) /Γ (1 - α)$ a…

q-fin.CP2016

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

Yuri M. Dimitrov, Lubin G. Vulkov

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 fin…

math.NA2016

Approximations for the Caputo derivative (II)

Yuri Dimitrov, Venelin Todorov, Radan Miryanov

In the present paper we use the expansion formula of the polylogarithm function to construct approximations of the Caputo derivative which are related to the midpoint approximation…