A New Grünwald-Letnikov Derivative Derived from a Second-Order Scheme

Efficient computation of the Grünwald-Letnikov fractional diffusion derivative using adaptive time step memory

Article history: Received 1 June 2014 Received in revised form 15 April 2015 Accepted 29 April 2015 Available online 5 May 2015

A numerical method for discrete fractional--order chemostat model derived from nonstandard numerical scheme

‎In this paper‎, ‎the fractional--order form of three dimensional chemostat model with variable yields is introduced‎. ‎The stability analysis of this fractional system is discussed in detail‎. ‎In order to study the dynamic behaviours of the mentioned fractional system‎, ‎the well known nonstandard (NSFD) scheme is implemented‎. ‎The proposed NSFD scheme is compared with the forward Euler and ...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.    

A Derivative-coderivative Inclusion in Second-order Nonsmooth Analysis

For twice smooth functions, the symmetry of the matrix of second partial derivatives is automatic and can be seen as the symmetry of the Jacobian matrix of the gradient mapping. For nonsmooth functions, possibly even extended-real-valued, the gradient mapping can be replaced by a subgradient mapping, and generalized second derivative objects can then be introduced through graphical differentiat...