Open Access Commentary

Open Access Original Research Article

An Accurate Implicit Quarter Step First Derivative Block Hybrid Method (AIQSFDBHM) for Solving Ordinary Differential Equations

P. Tumba, J. Sabo, A. A. Okeke, D. I. Yakoko

Asian Research Journal of Mathematics, Page 1-13
DOI: 10.9734/arjom/2019/v13i330106

The new accurate implicit quarter step first derivative blocks hybrid method for solving ordinary differential equations have been proposed in this paper via interpolation and collocation method for the solution of stiff ODEs. The analysis of the method was study and it was found to be consistent, convergent, zero-stability, We further compute the region of absolute stability region and it was found to be Aα − stable . It is obvious that, the numerical experiments considered showed that the methods compete favorably with existing ones. Thus, the pair of numerical methods developed in this research is computationally reliable in solving first order initial value problems, as the results from numerical solutions of stiff ODEs shows that this method is superior and best to solve such problems as in tables and figures.

Open Access Original Research Article

The Topp Leone Generalized Inverted Kumaraswamy Distribution: Properties and Applications

Hesham Reyad, Farrukh Jamal, Soha Othman, Nagla Yahia

Asian Research Journal of Mathematics, Page 1-15
DOI: 10.9734/arjom/2019/v13i330107

We propose a new four parameters continuous model called the Topp Leone generalized inverted Kumaraswamy distribution which extends the generalized inverted Kumaraswamy distribution. Basic mathematical properties of the new distribution are invstigated such as; quantile function, raw and incomplete moments, generating functions, probability weighted moments, order statistics, Rényi entropy, stochastic ordering and stress strength model. The method of maximum likelihood is used to estimate the model parameters of the new distribution. A Monte Carlo simulation is conducted to examine the behavior of the parameter estimates. The applicability of the new model is demonstrated by means of two real applications.

Open Access Original Research Article

Proposing a New Form of Fuzzy Sets and Its Properties

Einallah Salehi

Asian Research Journal of Mathematics, Page 1-10
DOI: 10.9734/arjom/2019/v13i330108

In this paper, a new form of fuzzy sets is defined, in which algebraic operations and some of their properties are different from algebraic operations on ordinary fuzzy sets. The definition provided enables us to examine the properties of fuzzy sets that are not possible using ordinary fuzzy sets.

Open Access Original Research Article

The Double Auxiliary Equations Method and its Application to Some Nonlinear Evolution Equations

A. A. Moussa, I. M. E. Abdelstar, A. K. Osman, L. A. Alhakim

Asian Research Journal of Mathematics, Page 1-11
DOI: 10.9734/arjom/2019/v13i330110

Throughout this article, symbolic computation will be used in order to construct a more general exact solutions of the nonlinear evolution equations through a new method called the double auxiliary equations' method, the method represent the study focus of this article. The method has proven applicable and practical through its applications to the generalized regularized long wave (RLW) equation and nonlinear Schrodinger equation.