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Journal of Applied & Computational Mathematics

ISSN: 2168-9679

Open Access

Current Issue

Volume 9, Issue 3 (2020)

    Research Pages: 1 - 6

    An Efficient Solver of Eigenmodes for a Class of Complex Optical Waveguides

    Jianxin Zhu* and Luying Li

    DOI: 10.4172/2168-9679.1000449

    In this paper, for a class of complex optical waveguide, the high-precision computation of the propagation constants β are studied. The corresponding Sturm-Liouville (S-L) problem is represented as 2 (,) (,) xz xz �? α �? β �? β�? zz z + += �?� �?� in an open domain (open on one side), where x is a given value. Firstly, a perfectly matched layer is used to terminate the open domain. Secondly, both the equation and the complex coordinate stretching transformations are constructed. Thirdly, the S-L problem is turned to a simplified form such as 2 ˆ ˆ ( )ˆ zz φ φ βφ + = s z in a bounded domain. Finally, the coefficient function s z( )ˆ is approximated by a piecewise polynomial of degree two. Since the simplified equation in each layer can be solved analytically by the Kummer functions, the approximate dispersion equation is established to the TE case. When the coefficient function is continuous, the approximate solutions converge fast to the exact ones, as the maximum value of the subinterval sizes tends to zero. Numerical simulations show that high-precision eigenmodes may be obtained by the Müller's method with suitable initial values.

    Research Pages: 1 - 7

    Matrix Representation of a Star

    Mohamed Moktar Chaffar

    DOI: 10.4172/2168-9679.1000448

    In the present paper we define an oriented Star with ??α coefficient α 1 and we further develop the procedure for finding eigenvalues and eigenvectors for an (5 × 5) Starmatrix directly or (5 × 5) Star-matrix indirectly. we give an overview of the methods to compute matrix-multiplication of a Star ??α (generally square 5 × 5) with particular emphasis on the oriented matrix

    Editor Note Pages: 1 - 2

    Editor Note on Journal of Applied and Computational Mathematics July

    Kyriaki Tsilika

    DOI: 10.4172/2168-9679.1000453

    The journal has been started in the year 2012 and it released its first volume in the same year. Till now, the journal has released 8 volumes by the end of 2019 and is successfully running its 9th Volume. The Journal is an open access publication that features scientific works of considerable significance and impact in all branches of mathematics that concerns with mathematical methods that are typically used in science, engineering, business, and industry. Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role in emphasizing algorithms

    Editor’s Note Pages: 1 - 2

    Editors Note on Applied and Computational Mathematics

    Guillermo Fernandez Anaya

    DOI: 10.4172/2168-9679.1000453

    The journal has been started in the year 2012 and it released its first volume in the same year. Till now, the journal has released 8 volumes by the end of 2019 and is successfully running its 9th Volume. The Journal is an open access publication that features scientific works of considerable significance and impact in all branches of mathematics that concerns with mathematical methods that are typically used in science, engineering, business, and industry. Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role in emphasizing algorithms, numerical methods and symbolic methods with the concept of ubiquitous computing. The journal provides an Open Access platform to analyse new computational and applied techniques for solving the scientific or engineering problems.

    Research Pages: 1 - 8

    Star with Coefficient a in the set of Real Numbers

    Mohamed Moktar Chaffar

    DOI: 10.4172/2168-9679.1000450

    This paper gives two definitions: Star with coefficient a real and Star System with coefficient α in five unknowns. Examples of Star-System and Star-set are given, a relationship between two star-Systems is noted, and some general theorems are proven.

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