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Koninklijke Vlaamse Ingenieursvereniging 2018 Journal of computational and applied mathematics Vol.333 No.-
<P><B>Abstract</B></P> <P>Fractional differential equations have been proved to be valuable tools for modeling diffusive processes associated with anomalous diffusion or spatial heterogeneity. However, many numerical methods for these equations have limitations in terms of computational efficiency due to the nonlocal nature of the fractional operator, which leads to large, dense matrices. The aim of this paper is to propose a second-order operator splitting Fourier spectral method as an accurate and efficient approach for solving fractional-in-space reaction–diffusion equations. This approach gives a full diagonal representation of the fractional operator and achieves spectral convergence regardless of the fractional power in the problem. In order to achieve second-order time accuracy, we decompose the original equation into linear and nonlinear subequations, and combine a half-time linear solver and a full-time second-order nonlinear solver followed by a final half-time linear solver. We numerically demonstrate the accuracy and efficiency of the proposed method and apply the proposed method to investigate the effect of the fractional power in fractional-in-space reaction–diffusion equations, including the Allen–Cahn, FitzHugh–Nagumo, and Gray–Scott models.</P>
A new approach to characterize the solution set of a pseudoconvex programming problem
Son, T.Q.,Kim, D.S. Koninklijke Vlaamse Ingenieursvereniging ; Elsevie 2014 Journal of computational and applied mathematics Vol.261 No.-
A new approach to characterize the solution set of a nonconvex optimization problem via its dual problem is proposed. Some properties of the Lagrange function associated to the problem are investigated. Then characterizations of the solution set of the problem are established.
Tail asymptotics of the queue size distribution in the M/M/m retrial queue
Kim, J.,Kim, J.,Kim, B. Koninklijke Vlaamse Ingenieursvereniging ; Elsevie 2012 Journal of computational and applied mathematics Vol.236 No.14
We consider an M/M/m retrial queue and investigate the tail asymptotics for the joint distribution of the queue size and the number of busy servers in the steady state. The stationary queue size distribution with the number of busy servers being fixed is asymptotically given by a geometric function multiplied by a power function. The decay rate of the geometric function is the offered load and independent of the number of busy servers, whereas the exponent of the power function depends on the number of busy servers. Numerical examples are presented to illustrate the result.
Hybridized SUPG and Upwind numerical schemes for convection dominated diffusion problems
Koninklijke Vlaamse Ingenieursvereniging 2015 Journal of computational and applied mathematics Vol.275 No.-
Hybridized numerical schemes for convection dominated diffusion equations are introduced. One is the upwind-penalty method (H-Upwind) and the other is the SUPG type method (H-SUPG). We provide stability analysis for both schemes and numerical experiments are presented to compare two suggested methods along with the standard SUPG finite element method.
Ren, Y.,Hu, L.,Sakthivel, R. Koninklijke Vlaamse Ingenieursvereniging ; Elsevie 2011 Journal of computational and applied mathematics Vol.235 No.8
This paper deals with the controllability of a class of impulsive neutral stochastic functional differential inclusions with infinite delay in an abstract space. Sufficient conditions for the controllability are derived with the help of the fixed point theorem for discontinuous multi-valued operators due to Dhage. An example is provided to illustrate the obtained theory.
Two-point <sup> G 1 </sup> Hermite interpolation in biangular coordinates
Ziatdinov, Rushan,Kim, Tae-wan,Nabiyev, Rifkat I. Koninklijke Vlaamse Ingenieursvereniging 2015 Journal of computational and applied mathematics Vol.287 No.-
<P><B>Abstract</B></P> <P>We construct <SUP> G 1 </SUP> Hermite interpolating curves in biangular coordinates, and provide sufficient conditions for their convexity. In a biangular coordinate system, the problem reduces to that of choosing suitable functions interpolating the biangular coordinates of the curve at its end points. The simplest linear equations, γ = ( ( 1 − t ) α , t β ) , in biangular coordinates correspond to a sectrix of Maclaurin, which we extend by introducing two shape parameters that pull the curve towards the sides of its triangular envelope. In addition, we consider a class of curves whose biangular coordinates have a constant sum, and we analyze their shape and curvature.</P> <P><B>Highlights</B></P> <P> <UL> <LI> The equations of most curves in biangular coordinate system are not yet known. </LI> <LI> We construct <SUP> G 1 </SUP> Hermite interpolating curves in biangular coordinates. </LI> <LI> Interpolation problem reduces to choosing suitable functions in biangular coordinates. </LI> <LI> The simplest linear equations correspond to the sectrix of Maclaurin. </LI> <LI> Proposed interpolation method may reduce the computational cost in some cases. </LI> </UL> </P> <P><B>Graphical abstract</B></P> <P>[DISPLAY OMISSION]</P>
Pathak, H.K.,Agarwal, R.P.,Cho, Y.J. Koninklijke Vlaamse Ingenieursvereniging ; Elsevie 2015 Journal of computational and applied mathematics Vol.283 No.-
In this paper, we consider some problems on coincidence point and fixed point theorems for multi-valued mappings. Applying the characterizations of P-functions, we establish some new existence theorems for coincidence point and fixed point distinct from Nadler's fixed point theorem, Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem and Du's fixed point theorem for nonlinear multi-valued contractive mappings in complete metric spaces. Our results compliment and extend the main results given by some authors in the literature. In the sequel, we consider a nonconvex integral inclusion and prove the Filippov type existence theorem by using an appropriate norm on the space of selection of a multi-function and a multi-valued contraction for set-valued mappings.
Comprehensive study of intersection curves in R<sup>4</sup> based on the system of ODEs
Hur, S.,Kim, T.w.,Bracco, C. Koninklijke Vlaamse Ingenieursvereniging ; Elsevie 2014 Journal of computational and applied mathematics Vol.256 No.-
We propose a new approach for the study of intersection curves c<SUB>I</SUB> in R<SUP>4</SUP> to obtain a general method for determining the Frenet frame {t,n,b<SUB>1</SUB>,b<SUB>2</SUB>} and curvatures κ<SUB>1</SUB>,κ<SUB>2</SUB>,κ<SUB>3</SUB> of c<SUB>I</SUB>. Our method is based on the theory of differential equations, which distinguishes it from the classical methods used in previous works [4-6] that were based mainly on differential geometry. Moreover, our method is suitable for any form of hypersurface that defines the intersection curves in R<SUP>4</SUP>.
The best G<sup>1</sup> cubic and G<sup>2</sup> quartic Bezier approximations of circular arcs
Hur, S.,Kim, T.w. Koninklijke Vlaamse Ingenieursvereniging ; Elsevie 2011 Journal of computational and applied mathematics Vol.236 No.6
We obtain cubic and quartic Bezier approximations of circular arcs that respectively satisfy G<SUP>1</SUP> and G<SUP>2</SUP> end-point interpolation conditions. We identify the necessary and sufficient conditions for such approximations to be the best, in the sense that they have the minimum Hausdorff distance to the circular arc. We then establish the existence and uniqueness of these best approximations and present practical methods to calculate them, which are verified by examples.
Negative dependence concept in copulas and the marginal free herd behavior index
Koninklijke Vlaamse Ingenieursvereniging 2015 Journal of computational and applied mathematics Vol.288 No.-
We provide a set of copulas that can be interpreted as having the negative extreme dependence. This set of copulas is interesting because it coincides with countermonotonic copula for a bivariate case, and more importantly, is shown to be minimal in concordance ordering in the sense that no copula exists which is strictly smaller than the given copula outside the proposed copula set. Admitting the absence of the minimum copula in multivariate dimensions greater than 2, the study of the set of minimal copulas can be important in the investigation of various optimization problems. To demonstrate the importance of the proposed copula set, we provide the variance minimization problem of the aggregated sum with arbitrarily given uniform marginals. As a financial/actuarial application of these copulas, we define a new herd behavior index using weighted Spearman's rho, and determine the sharp lower bound of the index using the proposed set of copulas.