In the present work, the numerical solution of two-dimensional variable-order fractional cable (VOFC) equation using meshless collocation methods with thin plate spline radial basis functions is considered. In the proposed methods, we first use two schemes of order O(τ2) for the time derivatives and then meshless approach is applied to the space component. Numerical results obtained ...

‎in this paper‎, ‎we present a new modification of chebyshev-halley‎ ‎method‎, ‎free from second derivatives‎, ‎to solve nonlinear equations‎. ‎the convergence analysis shows that our modification is third-order‎ ‎convergent‎. ‎every iteration of this method requires one function and‎ ‎two first derivative evaluations‎. ‎so‎, ‎its efficiency index is‎ ‎$3^{1/3}=1.442$ that is better than that o...

Introduction : Quite recently Chebyshev rational approximation to certain entire functions on the whole positive axis has attracted the attention of many mathematicians. In this respect the papers ([3-7, 9]) are worth mentioning. All these papers have been devoted only to entire functions of finite order. On the other hand, methods developed and used in these papers are valid only to entire fun...

The design of the optimal fuzzy fractional-order PID controller is addressed in this work. A multi-objective genetic algorithm is proposed to design rule base and membership functions of the fuzzy logic systems. Three conflicting objective functions in both time and frequency domains have been used in Pareto design of the fuzzy fractional-order PID controller. The simulation results reveal the ...

The mathematical theory of closed form functions for calculating LSFs on the basis of generating functions is presented. Exploiting recurrence relationships in the series expansion of Chebyshev polynomials of the first kind makes it possible to bootstrap iterative LSF-search from a set of characteristic polynomial zeros. The theoretical analysis is based on decomposition of sequences into symme...

We study the orthogonal polynomial expansion on sparse grids for a function of d variables in a weighted L space. A fast algorithm is developed to compute the orthogonal polynomial expansion by combining the fast cosine transform, a fast transform from the Chebyshev orthogonal polynomial basis to the orthogonal polynomial basis for the weighted L space, and a fast algorithm of computing hierarc...