4 papers
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 and second-order approxi…
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…
A Comparison Study of Two High Accuracy Numerical Methods for a Parabolic System in Air Pollution Modelling
Ivan Dimov, Juri Kandilarov, Venelin Todorov +1
We present two approaches for enhancing the accuracy of second order finite difference approximations of two-dimensional semilinear parabolic systems. These are the fourth order co…
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…