##### Bi-Level Multi-Objective Large Scale Integer Quadratic Programming Problem with Symmetric Trapezoidal Fuzzy Numbers in the Objective Functions

O. E. Emam, E. Fathy, A. A. Abdullah

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/JAMCS/2018/40808

This paper focuses on the solution of a Bi-Level Multi-Objective Large Scale Integer Quadratic Programming (BLMOLSIQP) problem, where all the decision parameters in the objective functions are symmetric trapezoidal fuzzy numbers, and have block angular structure of the constraints. The suggested algorithm based on α-level sets of fuzzy numbers, weighted sum method, Taylor’s series, Decomposition algorithm, and also the Branch and Bound method is used to find a compromised solution for the problem under consideration. Then, the proposed algorithm is compared to Frank and Wolfe algorithm to demonstrate its effectiveness. Moreover, the theoretical results are illustrated with the help of a numerical example.

##### Multidisemigraph Poset

Prabhakar R. Hampiholi, Meenal M. Kaliwal, Shailaja S. Shirkol, Jotiba P. Kitturkar

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/JAMCS/2018/39203

A semigraph is a generalization of a graph and is introduced by E. Sampathkumar. In this paper,,the concept of multidisemigraph, multidisemigraph poset (MDSPOSET) and various relations for a multidisemigraphs are defined with respect to the middle vertices and the end vertices. Also, the n - dimensional co-ordinate system is represented by using the concept of MDSPOSET.

##### An Implicit Method for Numerical Solution of System of First-Order Singular Initial Value Problems

M. Kamrul Hasan, M. Suzan Ahamed

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/JAMCS/2018/39745

Recently an implicit method has been developed for solving singular initial value problems numerically which have an initial singular point. The method is simple and gives significantly better results than the implicit Euler method as well as second order implicit Runge-Kutta (RK2) method. In this article, the system of first order singular initial value problems having an initial singular point has been solved by this method.

##### Global Analysis of a Directed Dynamics Competition Model

Md. Kamrujjaman, Kamrun Nahar Keya

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/JAMCS/2018/41247

In this study, we consider a directed-diffusion system describing the interactions between two organisms in heterogeneous environment. We focus on the effects of two distribution functions while two species are distributed with their corresponding resource function. We determine the global asymptotic stability of semi-trivial as well as the coexistence steady states due to interactions among three smooth functions.

##### Differential Transform Decomposition Method for the Solution of Boundary Layer Equations in a Finite Domain

R. A. Oderinu, F. O. Akinpelu, Y. A. S. Aregbesola

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/JAMCS/2018/40159

A new method called differential transform decomposition method (DTDM) for solving differential equations was developed. This method was derived by coupling the scheme of Differential Transform with Adomain polynomials,the necessity of the Adomian polynomial is to decompose the the non linear functions existing in a differential equation so that the differential transform of such functions could be obtained easily.To validate the efficiency of the proposed method, a single and coupled boundary value problems in a finite domain were considered. The results obtained were presented in a polynomial form so that the solution at any point of the problems considered could be obtained as against some methods which are discritised. Computational results agree with the referenced solution for the single boundary value problem and for the coupled boundary value problems the results agrees with that of the weighted residual method.