Matrix Science Mathematic (MSMK)

LAGUERRE POLYNOMIALS SOLUTION FOR SOLVING HIGH-ORDER DELAY LINEAR DIFFERENTIAL EQUATIONS

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msmk.01.2020.27.31

ABSTRACT

LAGUERRE POLYNOMIALS SOLUTION FOR SOLVING HIGH-ORDER DELAY LINEAR DIFFERENTIAL EQUATIONS

Journal: Matrix Science Mathematic (MSMK)
Author: Mohamed El-Gamel, Walid Tharwat, Magdy El-Azab

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2020.27.31

The aim of this article is to present an efficient numerical procedure for solving higher-order linear delay differential equations with variable coefficients under the mixed conditions in terms of Laguerre polynomials. Four problems are solved and results are compared with the existing results to show the accuracy and applicability of Laguerre polynomials.
Pages 27-31
Year 2020
Issue 1
Volume 4

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msmk.01.2020.20.26

ABSTRACT

CUBIC B-SPLINE SOLUTION FOR A SECOND-ORDER SINGULAR LINEAR PARTIAL DIFFERENTIAL EQUATIONS

Journal: Matrix Science Mathematic (MSMK)
Author: Mohamed El-Gamel, Neveen El-Shamy

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2020.20.26

A new approach implementing the cubic B-spline technique is introduced for the numerical solution of a class of singular partial differential equation. Properties of these cubic B-spline functions are first presented. These properties are then used to reduce singular partial differential equation to systems of linear algebraic equations. Numerical examples illustrate the pertinent features of the method and its applicability to a large variety of problems. The examples include regular and singular problems.
Pages 20-26
Year 2020
Issue 1
Volume 4

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msmk.01.2020.14.19

ABSTRACT

COMPUTATION OF THE POWER OF BASE OF TWO DIGITS NUMBER USING KIFILIDEEN (MATRIX, COMBINATION AND DISTRIBUTIVE (MCD)) APPROACH

Journal: Matrix Science Mathematic (MSMK)
Author: Kifilideen L. Osanyinpeju

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2020.14.19

The different methods used in the multiplication of numbers are long method (column method) of multiplication, grid methods and addition methods of multiplication. The utilization of the methods mentioned to solve power (index) of base number (number that multiply itself in a number of times) are horrendous, outrageous, tedious, time consuming and too long to be carried out. This study develops computation of the power of base of number using Kifilideen (matrix, combination and distributive (MCD)) approach. The Kif matrix method of multiplication is a shorter version of the long method (column method) of multiplication. The matrix method provides a straight forward, direct and systematic means of multiplication of digit number that multiply itself repetitively.
Pages 14-19
Year 2020
Issue 1
Volume 4

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msmk.01.2020.10.13

ABSTRACT

ANALYTICAL APPROXIMATION FOR THE NONLINEAR DYNAMICS OF ERK ACTIVATION IN THE PRESENCE OF COMPETITIVE INHIBITOR

Journal: Matrix Science Mathematic (MSMK)
Author: Yudi Ari Adi, M. Irawan Jayadi, Agung Budiantoro

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2020.10.13

The extracellular signal-regulated protein kinase (ERK), a subfamily of Mitogen-Activated Protein Kinase (MAPK) pathways, is one of the most important signals in the regulation of many biological processes. Deregulated of MAPK signaling pathways has been observed in human cancers with potential involvement in most of all cellular processes leading to tumorigenesis so that it became a potential target for therapy in cancer patients. In this paper, we discuss a Mathematical model of ERK activation in the presence of a small molecule inhibitor that competes with RAS. We present analytical expressions for the concentration of RAS, complex RAS-ERK, complex RAS-Inhibitor, and activated ERK in terms of dimensionless parameters using He’s Homotopy Perturbation Method (HPM). The analytical results are compared with numerical simulation and satisfactory agreement is obtained.
Pages 10-13
Year 2020
Issue 1
Volume 4

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msmk.01.2020.06.09

ABSTRACT

ON NEW WAYS OF VARIOUS IDEALS IN TERNARY SEMIGROUPS

Journal: Matrix Science Mathematic (MSMK)
Author: M. Palanikumar, K. Arulmozhi

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2020.06.09

We discuss tri-quasi ideals and bi-quasi ideals in ternary semigroups and give some characterizations. The intersection of left, lateral and right ideals is a tri-ideal and product of left, lateral and right ideals is again a tri-ideal. We also discuss m-tri-ideals towards some characterizations in terms of tri-ideals. Some relevant counter examples are also indicated.
Pages 06-09
Year 2020
Issue 1
Volume 4

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msmk.01.2020.01.05

ABSTRACT

ANALYTIC APPROXIMATE SOLUTION OF RABIES TRANSMISSION DYNAMICS USING HOMOTOPY PERTURBATION METHOD

Journal: Matrix Science Mathematic (MSMK)
Author: Muhammad Sinan

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2020.01.05

In this paper, we consider a mathematical model of Rabies disease which is an infectious disease. The model we are considering is a system of nonlinear ordinary differential equations and it is difficult to find an exact solution. He’s Homotopy perturbation method is employed to compute an approximation to the solution of the system of nonlinear ordinary differential equations. The findings obtained by HPM are compared with a nonstandard finite difference (NSFD) and Runge-Kutta fourth order (RK4) methods. Some plots are presented to show the reliability and simplicity of the method.
Pages 1-5
Year 2020
Issue 1
Volume 4

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msmk.02.2019.17.21

ABSTRACT

FINITE ELEMENT METHOD FOR SOLVING NONLINEAR RANDOM ORDINARY DIFFERENTIAL EQUATIONS

Journal: Matrix Science Mathematic (MSMK)
Author: Ibrahim Elkott, Ibrahim.L. El-Kalla, Ahmed Elsaid, Reda Abdo

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2019.17.21

In this paper we utilize the finite element method for solving random nonlinear differential equations. In the proposed technique, the nodal coefficients are formulated as functions of the random variable. At certain values of random variable, curve fitting is used to construct the approximate nodal solution. Several numerical examples are presented, and the approximate mean solutions are compared with the exact mean solution to illustrate the ability and effectiveness of this method.
Pages 17-21
Year 2019
Issue 2
Volume 3

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msmk.02.2019.11.16

ABSTRACT

LAPLACE ADOMIAN DECOMPOSITION METHOD FOR SOLVING A MODEL OF CHRONIC MYELOGENOUS LEUKEMIA (CML) AND T CELL ASSOCIATION

Journal: Matrix Science Mathematic (MSMK)
Author: Faiz Alam

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2019.11.16

In this article, it is our purpose that we examine as well as analyze Chronic Myelogenous Leukemia (CML) a mathematical model, a white blood cells cancer. This model shows the association between naive T cells, effector T cells and CML cancer cells in the body, using a system of differential equations which give the rate of change of these three-cell population. We implement a Laplace Adomian Decomposition Method to compute an approximate solution of the considered model. We try to obtain analytic solution for CML model in the form of series that rapidly converges. Further, we also provide some result and stability of the propose model.
Pages 11-16
Year 2019
Issue 2
Volume 3

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msmk.02.2019.08.10

ABSTRACT

ON THE MATLAB TECHNIQUE BY USING LAPLACE TRANSFORM FOR SOLVING SECOND ORDER ODE WITH INITIAL CONDITIONS EXACTLY

Journal: Matrix Science Mathematic (MSMK)
Author: Bawar Mohammed Faraj and Faraedoon Waly Ahmed

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.02.2019.08.10

In this paper Matlab technique has been presented that is approach to exact solution for second order ODE with constant coefficients and initial condition by using Laplace transformation. Matlab function has been constructed to estimate and compute exact solution of second order ordinary differential equations with initial conditions generally, the results of the program shows the elapsed time, exact solution and it’s figures.
Pages 8-10
Year 2019
Issue 2
Volume 3

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msmk.01.2019.20.24

ABSTRACT

ANALYTICAL APPROXIMATE SOLUTION OF NON-LINEAR PROBLEM BY HOMOTOPY PERTURBATION METHOD (HPM)

Journal: Matrix Science Mathematic (MSMK)
Author: Ihtisham ul Haq

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DOI: 10.26480/msmk.01.2019.20.24

In this article, we want to find the analytic approximate solution of nonlinear problems by using Homotopy Perturbation Method. Using the Homotopy Perturbation Method once we express the nonlinear problem into infinite number of sub linear problems and then obtain the solution of linear problems.
Pages 20-24
Year 2019
Issue 1
Volume 3

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