Yuri M. Dimitrov

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20132018

most citedNumerical Approximations for Fractional Differential Equations

51 citations · 94 across the 10 of their papers we have counts for

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Showing 2016Show all

4 papers · 1 filter

math.NA2016★ 8 cited

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★ 6 cited

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…

math.NA2016★ 5 cited

Higher-Order Numerical Solutions of the Fractional Relaxation-Oscillation Equation using Fractional Integration

Yuri Dimitrov

In the present paper we derive the asymptotic expansion formula for the trapezoidal approximation of the fractional integral. We use the expansion formula to obtain approximations…