Add to ORKGWe present an extrapolation type algorithm for the numerical solution of fractional order differential equations. It is based on the new result that the sequence of approximate solutions of these equations, computed by means of a recently published algorithm by Diethelm [6], possesses an asymptotic expansion with respect to the stepsize. From this we conclude that the application of extrapolation is justified, and we obtain a very efficient differential equation solver with practically no additional numerical costs. This is also illustrated by a number of numerical examples
This paper discusses the development of efficient algorithms for a certain fractional differential e...
Given a system of fist order differential equations, whose coefficient matrix has constant elements,...
Taking into account the regularity properties of the solutions of fractional differential equations,...
We present an extrapolation type algorithm for the numerical solution of fractional order differenti...
We present an extrapolation type algorithm for the numerical solution of fractional order differenti...
An extrapolation algorithm is considered for solving linear fractional differential equations in thi...
This paper uses polynomial interpolation to design a novel high-order algorithm for the numerical es...
This thesis explores higher order numerical methods for solving fractional differential equations
In this paper, we present a new numerical method to solve fractional differential equations. Given ...
In this dissertation, we consider numerical methods for solving fractional differential equations wi...
The final publication is available at Springer via http://dx.doi.org/10.1007/s10543-013-0443-3In thi...
In this paper we consider the numerical solution of fractional differential equations by means of m-...
There has recently been considerable interest in using a nonstandard piecewise approximation to form...
In this paper, we first introduce an alternative proof of the error estimates of the numerical metho...
This is a PDF version of an preprint submitted to Elsevier. The definitive version was published in ...
This paper discusses the development of efficient algorithms for a certain fractional differential e...
Given a system of fist order differential equations, whose coefficient matrix has constant elements,...
Taking into account the regularity properties of the solutions of fractional differential equations,...
We present an extrapolation type algorithm for the numerical solution of fractional order differenti...
We present an extrapolation type algorithm for the numerical solution of fractional order differenti...
An extrapolation algorithm is considered for solving linear fractional differential equations in thi...
This paper uses polynomial interpolation to design a novel high-order algorithm for the numerical es...
This thesis explores higher order numerical methods for solving fractional differential equations
In this paper, we present a new numerical method to solve fractional differential equations. Given ...
In this dissertation, we consider numerical methods for solving fractional differential equations wi...
The final publication is available at Springer via http://dx.doi.org/10.1007/s10543-013-0443-3In thi...
In this paper we consider the numerical solution of fractional differential equations by means of m-...
There has recently been considerable interest in using a nonstandard piecewise approximation to form...
In this paper, we first introduce an alternative proof of the error estimates of the numerical metho...
This is a PDF version of an preprint submitted to Elsevier. The definitive version was published in ...
This paper discusses the development of efficient algorithms for a certain fractional differential e...
Given a system of fist order differential equations, whose coefficient matrix has constant elements,...
Taking into account the regularity properties of the solutions of fractional differential equations,...