Open Access Original Research Article

Exact Solutions and Rogue Waves for the Derivative Nonlinear SchrÖdinger Equation

Changfu Liu, Jinmei Liu, Ping Zhou

Journal of Advances in Mathematics and Computer Science, Page 1-6
DOI: 10.9734/jamcs/2019/v31i630127

Exact solutions which contain periodic solutions, soliton solutions and rogue wave solutions for two the modied derivative nonlinear Schrodinger equations, are obtained by means of solutions of a known derivative nonlinear SchrÖdinger equation. Two solutions' images are displayed, which can help one understand their dynamical behavior better. These results enrich the solutions' structural diversity for the modied derivative nonlinear schrÖdinger equations.

Open Access Original Research Article

A Family of High Order One-Block Methods for the Solution of Stiff Initial Value Problems

I. J. Ajie, K. Utalor, P. Onumanyi

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/jamcs/2019/v31i630128

In this paper, we construct a family of high order self-starting one-block numerical methods for the solution of stiff initial value problems (IVP) in ordinary differential equations (ODE). The Reversed Adams Moulton (RAM) methods, Generalized Backward Differentiation Formulas (GBDF) and Backward Differentiation Formulas (BDF) are used in the constructions. The E-transformation is applied to the triples and a family of self-starting methods are obtained. The family is for . The numerical implementation of the methods on some stiff initial value problems are reported to show the effectiveness of the methods. The computational rate of convergence tends to the theoretical order as h tends to zero.

Open Access Original Research Article

Penalty Algorithm Based on Three-Term Conjugate Gradient Method for Unconstrained Optimization Portfolio Management Problems

Samson Akinwale, O. O. Okundalaye

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/jamcs/2019/v31i630129

In a class of solving unconstrained optimization problems, the conjugate gradient method has been proved to be efficient by researchers' due to it's smaller storage requirements and computational cost. Then, a class of penalty algorithms based on three-term conjugate gradient methods was developed and extend to and solution of an unconstrained minimization portfolio management problems, where the objective function is a piecewise quadratic polynomial. By implementing the proposed algorithm to solve some selected unconstrained optimization problems, resulted in improvement in the total number of iterations and CPU time. It was shown that this algorithm is promising.

Open Access Original Research Article

Statistical Analysis of the Mixture of Inverted Exponential Distribution Under Bayesian Approach

Tabasam Sultana, Muhammad Aslam, Javid Shabbir

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/jamcs/2019/v31i630130

This paper is about studying a 3-component mixture of the Inverted Exponential distributions under Bayesian view point. The type-I right censored sampling scheme is considered because of its extensive use in reliability theory and survival analysis. The expressions for the Bayes estimators and their posterior risks are derived under dierent loss scenarios. In case, no or little prior information is available, elicitation of hyper parameters is given. In order to study numerically, the execution of the Bayes estimators under dierent loss functions, their statistical properties have been simulated for dierent sample sizes and test termination times. A real life data example is given to illustrate the study. Graphical representation of the simulation analysis results is also given to study the properties of the Bayes estimators.

Open Access Original Research Article

Methods of Bilateral Approximations for Nonlinear Eigenvalue Problems

Bohdan Podlevskyi

Journal of Advances in Mathematics and Computer Science, Page 1-20
DOI: 10.9734/jamcs/2019/v31i630131

In this article, the research proposed by the author, the approach to the construction of methods and algorithms of bilateral approximations to the eigenvalues of nonlinear spectral problems, is continued. On the basis of Newton's method, some new algorithms of the bilateral approximations to their eigenvalues are constructed and substantiated.