Journal•ISSN: 0377-0427

# Journal of Computational and Applied Mathematics

About: Journal of Computational and Applied Mathematics is an academic journal. The journal publishes majorly in the area(s): Numerical analysis & Nonlinear system. It has an ISSN identifier of 0377-0427. Over the lifetime, 13497 publication(s) have been published receiving 274103 citation(s).

Topics: Numerical analysis, Nonlinear system, Boundary value problem, Finite element method, Differential equation

##### Papers published on a yearly basis

##### Papers

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TL;DR: A new graphical display is proposed for partitioning techniques, where each cluster is represented by a so-called silhouette, which is based on the comparison of its tightness and separation, and provides an evaluation of clustering validity.

Abstract: A new graphical display is proposed for partitioning techniques. Each cluster is represented by a so-called silhouette, which is based on the comparison of its tightness and separation. This silhouette shows which objects lie well within their cluster, and which ones are merely somewhere in between clusters. The entire clustering is displayed by combining the silhouettes into a single plot, allowing an appreciation of the relative quality of the clusters and an overview of the data configuration. The average silhouette width provides an evaluation of clustering validity, and might be used to select an ‘appropriate’ number of clusters.

10,821 citations

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Abstract: A family of embedded Runge-Kutta formulae RK5 (4) are derived. From these are presented formulae which have (a) ‘small’ principal truncation terms in the fifth order and (b) extended regions of absolute stability.

2,589 citations

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TL;DR: A new definition of fractional derivative and fractional integral is given and it is shown that it is the most natural definition, and the most fruitful one.

Abstract: We give a new definition of fractional derivative and fractional integral. The form of the definition shows that it is the most natural definition, and the most fruitful one. The definition for [email protected][email protected]<1 coincides with the classical definitions on polynomials (up to a constant). Further, if @a=1, the definition coincides with the classical definition of first derivative. We give some applications to fractional differential equations.

1,390 citations

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Abstract: Fractional advection-dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper we develop practical numerical methods to solve one dimensional fractional advection-dispersion equations with variable coefficients on a finite domain. The practical application of these results is illustrated by modeling a radial flow problem. Use of the fractional derivative allows the model equations to capture the early arrival of tracer observed at a field site.

1,198 citations

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TL;DR: The basic concepts in this new simple interesting fractional calculus called conformable fractional derivative are set and the fractional versions of chain rule, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions, Laplace transforms and linear differential systems are proposed and discussed.

Abstract: Recently, the authors Khalil et?al. (2014) introduced a new simple well-behaved definition of the fractional derivative called conformable fractional derivative. In this article we proceed on to develop the definitions there and set the basic concepts in this new simple interesting fractional calculus. The fractional versions of chain rule, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions, Laplace transforms and linear differential systems are proposed and discussed.

978 citations