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 2015 · math.NAShow all

3 papers · 2 filters

math.NA2015★ 6 cited

Three-Point Compact Approximation for the Caputo Fractional Derivative

Yuri Dimitrov

In this paper we derive the fourth-order asymptotic expansions of the trapezoidal approximation for the fractional integral and the $L 1$ approximation for the Caputo derivative. We…

math.NA2015★ 2 cited

A New Method for Numerical Solution of the Fractional Relaxation and Subdiffusion Equations Using Fractional Taylor Polynomials

Yuri Dimitrov

The accuracy of the numerical solution of a fractional differential equation depends on the differentiability class of the solution. The derivatives of the solutions of fractional…

math.NA2015★ 15 cited

A Second Order Approximation for the Caputo Fractional Derivative

Yuri Dimitrov

When $0 < α < 1$ , the approximation for the Caputo derivative $y^{(α)} (x) = \frac{1}{Γ ( 2 - α ) h ^{α}} k = 0 \sum n σ_{k}^{(α)} y (x - k h) + O (h^{2 - α}),$ where $σ_0^{(α)} = 1, σ_n^{(α)} =…