American Journal of Computational Mathematics

Journal Information
ISSN / EISSN : 21611203 / 21611211
Current Publisher: Scientific Research Publishing, Inc. (10.4236)
Total articles ≅ 351
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Latest articles in this journal

Enoch Suleiman, M. S. Audu
American Journal of Computational Mathematics, Volume 10, pp 23-30; doi:10.4236/ajcm.2020.101002

Abstract:This paper computes the group and character table of Trimethylborane and Cyclohaxane. Results show that the groups are isomorphic to the wreath products C3wrC2 and C2wrC6 with orders 81 and 384 and with 17 and 28 conjugacy classes respectively, where Cn denotes a cyclic group of order n.
Tsegay Giday Woldu, Haibin Zhang, Yemane Hailu Fissuh
American Journal of Computational Mathematics, Volume 10, pp 1-22; doi:10.4236/ajcm.2020.101001

Abstract:In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmonotone line search technique. The method incorporates the modified BFGS secant equation in an effort to include the second order information of the objective function. The new secant equation has both gradient and function value information, and its update formula inherits the positive definiteness of Hessian approximation for general convex function. In order to improve the likelihood of finding a global optimal solution, we introduce a new modified nonmonotone line search technique. It is shown that, for nonsmooth convex problems, the proposed algorithm is globally convergent. Numerical results show that this new scaled conjugate gradient algorithm is promising and efficient for solving not only convex but also some large scale nonsmooth nonconvex problems in the sense of the Dolan-Moré performance profiles.
Abeer A. Alshareef, H. A. Batarfi
American Journal of Computational Mathematics, Volume 10, pp 31-42; doi:10.4236/ajcm.2020.101003

Abstract:In this paper, the global stability of free smoking equilibrium point was evaluated and presented graphically. The linear stability of a developed mathematical model illustrates the effect on the population of chain, mild and passive smokers. MATLAB programming was used to simulate the solutions, the reproduction number R0 and the nature of the equilibria.
Nhan T. Tran
American Journal of Computational Mathematics, Volume 9, pp 201-206; doi:10.4236/ajcm.2019.93015

Abstract:In this paper, we study the class of one-dimensional singular integrals that converge in the sense of Cauchy principal value. In addition, we present a simple method for approximating such integrals.
E. Omokhuale, M. L. Jabaka, Omokhuale E., L. Jabaka M.
American Journal of Computational Mathematics, Volume 9, pp 187-200; doi:10.4236/ajcm.2019.93014

Abstract:In this paper, the fluid examined was electrically conducting. The presence of a uniform transverse magnetic field at the plate was also taken into cognizance. The flow was governed by a modeled coupled nonlinear system of partial differential equations (PDEs) in dimensional form which was transformed into non-dimensional form using some non-dimensional variables. Explicit finite difference method (EFDM) was employed to approximate the fluid velocity, temperature and concentration. The effects of embedded thermo physical parameters of engineering interests on the flow quantities viz. velocity, temperature, concentration field presented through graphs were also examined through a series of numerical experiments and discussed. During the course of the numerical computations, it was found that heat generation has a tendency to enhance the fluid velocity as an opposite result is seen with chemical reaction parameter. A comparison was conducted of present results with the previous literature to show the accuracy of the results.
Yunxia Ren, Shiying Wang
American Journal of Computational Mathematics, Volume 9, pp 133-142; doi:10.4236/ajcm.2019.93010

Abstract:The diagnosability of a multiprocessor system or an interconnection network is an important research topic. The system and an interconnection network have an underlying topology, which is usually presented by a graph. In this paper, we show proof for the g-good-neighbor diagnosability of the exchanged hypercube EH (s,t) under the PMC model and MM* model.
Philip Ajibola Bankole, Olabisi O. Ugbebor
American Journal of Computational Mathematics, Volume 9, pp 143-157; doi:10.4236/ajcm.2019.93011

Abstract:A Fast Fourier transform approach has been presented by Carr & Madan (2009) on a single underlying asset. In this current research paper, we present fast Fourier transform algorithm for the valuation of Multi-asset Options under Economic Recession Induced Uncertainties. The issue of multi-dimension in both finite and infinite case of Options is part of the focus of this research. The notion of economic recession was incorporated. An intuition behind the introduction of recession induced volatility uncertainty is revealed by huge volatility variation during the period of economic recession compared to the period of recession-free. Nigeria economic recession outbreak in 2016 and its effects on the uncertainty of the payoffs of Nigeria Stocks Exchange (NSE) among other investments was among the motivating factors for proposing economic recession induced volatility in options pricing. The application of the proposed Fast Fourier Transform algorithm in handling multi-assets options was shown. A new result on options pricing was achieved and capable of yielding efficient option prices during and out of recession. Numerical results were presented on assets in 3-dimensions as an illustration taking Black Scholes prices as a bench mark for method effectiveness comparison. The key findings of this research paper among other crucial contributions could be seen in computational procedure of options valuation in multi-dimensions and uncertainties in options payoffs under the exposure of economic recession.
Jannatun Nayeem, Israt Sultana
American Journal of Computational Mathematics, Volume 9, pp 158-173; doi:10.4236/ajcm.2019.93012

Abstract:We develop a dynamical model to understand the underlying dynamics of TUBERCULOSIS infection at population level. The model, which integrates the treatment of individuals, the infections of latent and recovery individuals, is rigorously analyzed to acquire insight into its dynamical features. The phenomenon resulted due to the exogenous infection of TUBERCULOSIS disease. The mathematical analysis reveals that the model exhibits a backward bifurcation when TB treatment remains of infected class. It is shown that, in the absence of treatment, the model has a disease-free equilibrium (DEF) which is globally asymptotically stable (GAS) and the associated reproduction threshold is less than unity. Further, the model has a unique endemic equilibrium (EEP), for a special case, whenever the associated reproduction threshold quantity exceeds unity. For a special case, the EEP is GAS using the central manifold theorem of Castillo-Chavez.
Na Zhu, Meiling Zhao
American Journal of Computational Mathematics, Volume 9, pp 174-186; doi:10.4236/ajcm.2019.93013

Abstract:We present a fourth-order finite difference scheme for the Helmholtz equation in polar coordinates. We employ the finite difference format in the interior of the region and derive a nine-point fourth-order scheme. Specially, ghost points outside the region are applied to obtain the approximation for the Neumann boundary condition. We obtain the matrix form of the linear system and the sparsity of the coefficient matrix is favorable for the computation of the Helmholtz equation. The feasibility and accuracy of the method are validated by two test examples which have exact solutions.
Wan Zhang, Hang Yang, Liping Liu
American Journal of Computational Mathematics, Volume 9, pp 32-47; doi:10.4236/ajcm.2019.92003

Abstract:It is well known that the full compressible Navier-Stokes equations with viscosity and heat conductivity coefficients of order of the Knudsen number ò>0 can be deduced from the Boltzmann equation via the Chapman-Enskog expansion. In this paper, we carry out the rigorous mathematical study of the compressible Navier-Stokes equation with the initial-boundary value problems. We construct the existence and most importantly obtain the higher regularities of the solutions of the full compressible Navier-Stokes system with weak viscosity and heat conductivity in a general bounded domain.