##### International Journal of Mathematical Sciences and Computing (IJMSC)

IJMSC Vol. 5, No. 3, Jul. 2019

#### MECS Press Journal

REGULAR PAPERS

##### A Numerical Approach for Solving High-Order Boundary Value Problems

DOI: https://doi.org/10.5815/ijmsc.2019.03.01, Pub. Date: 8 Jul. 2019

In this paper, a numerical method which produces an approximate solution is presented for the numerical solutions of sixth,eighth,ninth and twelfth order boundary value problems. With the aid of derivatives of power series which slightly perturbe and collocate, eventually converts boundary value problems into the square matrix equations with the unknown coefficients obtain using MAPLE 18 software. This method gives the approximate solutions and compare with the exact solutions. Finally, some examples and their numerical solutions are given by comparing the numerical results obtained to other methods available in the literature, show a good agreement and efficiency.

##### Periodic Pattern Formation Analysis Numerically in a Chemical Reaction-Diffusion System

DOI: https://doi.org/10.5815/ijmsc.2019.03.02, Pub. Date: 8 Jul. 2019

In this paper, we analyze the pattern formation in a chemical reaction-diffusion Brusselator model. Twocomponent Brusselator model in two spatial dimensions is studied numerically through direct partial differential equation simulation and we find a periodic pattern. In order to understand the periodic pattern, it is important to investigate our model in one-dimensional space. However, direct partial differential equation simulation in one dimension of the model is performed and we get periodic traveling wave solutions of the model. Then, the local dynamics of the model is investigated to show the existence of the limit cycle solutions. After that, we establish the existence of periodic traveling wave solutions of the model through the continuation method and finally, we get a good consistency among the results.

##### Randamization Technique for Desiging of Substitution Box in Data Encryption Standard Algorithm

DOI: https://doi.org/10.5815/ijmsc.2019.03.03, Pub. Date: 8 Jul. 2019

A new approach for the generation of randomized substitution box (S-box) based on the concept of a redesign of S-box with fewer numbers of input bits processed at a time as compared to existing S-box in Data Encryption Standard (DES) Algorithm. The results of experimentation prove that proposed randomized approach also generate promising results, which can be particularly useful for devices with less processing power. Proposed approach retains the diffusion and confusion property of a good cryptosystem algorithm.

##### Mining Maximal Subspace Clusters to deal with Inter-Subspace Density Divergence

DOI: https://doi.org/10.5815/ijmsc.2019.03.04, Pub. Date: 8 Aug. 2019

In general, subspace clustering algorithms identify enormously large number of subspace clusters which may possibly involve redundant clusters. This paper presents Dynamic Epsilon based Maximal Subspace Clustering Algorithm (DEMSC) that handles both redundancy and inter-subspace density divergence, a phenomenon in density based subspace clustering. The proposed algorithm aims to mine maximal and non-redundant subspace clusters. A maximal   subspace cluster is defined by a group of similar data objects that share maximal number of attributes. The DEMSC algorithm consists of four steps. In the first step, data points are assigned with random unique positive integers called labels. In the second step, dense units are identified based on the density notion using proposed dynamically computed epsilon-radius specific to each subspace separately and user specified input parameter minimum points, τ.  In the third step, sum of the labels of each data object forming the dense unit is calculated to compute its signature and is hashed into the hash table. Finally, if a dense unit of a particular subspace collides with that of the other subspace in the hash table, then both the dense units exists with high probability in the subspace formed by combining the colliding subspaces. With this approach efficient maximal subspace clusters which are non-redundant are identified and outperforms the existing algorithms in terms of cluster quality and number of the resulted subspace clusters when experimented on different benchmark datasets.