Frequency: Quarterly E- ISSN: 2277-2243 P- ISSN: Awaited Abstracted/ Indexed in: Ulrich's International Periodical Directory, Google Scholar, SCIRUS, Genamics JournalSeek, EBSCO Information Services
Quarterly published in print and online "Inventi Impact: Computational Mathematics" publishes high quality unpublished as well as high impact pre-published research and reviews catering to the needs of mathematicians and professional engineers. The journal is interdisciplinary and deals with multiple aspects of computation mathematics including numerical methods, algorithms, numerical logics, number theory, algebraic calculations and computational statistics.
The most intense and catastrophic hurricanes on record to hit the Florida\nKeys during 1900 to 1950 were in 1919, and 1935. From 1950 to 2000, the\nmost intense hurricanes to hit or affect the Florida Keys were in 1960, 1965,\nand 1992. In this paper, we will present a brief parametric analysis of the hurricanes\nthat have hit the Florida Keys in the last 100 years. This analysis will\ninclude the descriptive statistics, best fit probability distribution of the latitude\nof the catastrophic hurricanes and a confidence interval that detects the average\nlatitude of hurricanes (category 3 or higher) which have hit the Florida\nKeys in the last 100 years....
ThispapermainlypresentsEulermethodandfourthorderRungeKuttaMethod(RK4)forsolving\ninitialvalueproblems(IVP)forordinarydifferentialequations(ODE).Thetwoproposedmethods\narequiteefficientandpracticallywellsuitedforsolvingtheseproblems.Inordertoverifytheac\ncuracy,wecomparenumericalsolutionswiththeexactsolutions.Thenumericalsolutionsarein\ngood agreement with the exact solutions. Numerical comparisons between Euler method and\nRungeKuttamethodhavebeenpresented.Alsowecomparetheperformanceandthecomputa\ntional effort of suchmethods. In order to achieve higher accuracy in the solution, the step size\nneedstobeverysmall.Finallyweinvestigateandcomputetheerrorsofthetwoproposedmeth\nodsfordifferentstepsizestoexaminesuperiority.Severalnumericalexamplesaregiventodem\nonstratethereliabilityandefficiency....
For ordinal log-linear models, the estimation of the parameter reflecting the linear-by-linear measure of association has long been\r\na topic for the analysis of dependence for contingency tables. Typically, iterative procedures (including Newtonââ?¬â?¢s method) are used\r\nto determine the maximum likelihood estimate of the parameter. Recently Beh and Farver (2009, ANZJS, 51, 335ââ?¬â??352) show by\r\nway of example three reliable and accurate noniterative techniques that can be used to estimate the parameter and extended this\r\nstudy by examining their reliability computationally. This paper further investigates the reliability of the non-iterative procedures\r\nwhen compared with Newtonââ?¬â?¢s method for estimating this association parameter and considers the impact of the sample size on\r\nthe estimate....
In this article, we numerically investigate a two-dimensional (2D) droplet deformation and breakup in simple shear flow using a phase-field model for two-phase fluid flows. The dominant driving force for a droplet breakup in simple shear flow is the three-dimensional (3D) phenomenon via surface tension force and Rayleigh instability, where a liquid cylinder of certain wavelengths is unstable against surface perturbation and breaks up into individual droplets to reduce the total surface energy. A 2D droplet breakup does not occur except in special cases because there is only one curvature direction of the droplet interface, which resists breakup. However, there have been many numerical simulation research works on the 2D droplet breakups in simple shear flow. This study demonstrates that the 2D droplet breakup phenomenon in simple shear flow is due to the lack of space resolution of the numerical grid....
In this paper, we study the problem of solving Seal’s type partial integro-differential equations (PIDEs) for the classical compound Poisson risk model. A data-driven deep neural network (DNN) method is proposed to calculate finite-time survival probability, and an alternative scheme is also investigated when claim payments are exponentially distributed. The DNN method is then extended to the numerical solution of generalized PIDEs. Numerical approximation results under different claim distributions are given, which show that the proposed scheme can obtain accurate results under different claim distributions....
We propose a conjugate gradient method which is based on the study of the Dai-Liao conjugate gradient method. An important\r\nproperty of our proposed method is that it ensures sufficient descent independent of the accuracy of the line search. Moreover, it\r\nachieves a high-order accuracy in approximating the second-order curvature information of the objective function by utilizing the\r\nmodified secant condition proposed by Babaie-Kafaki et al. (2010). Under mild conditions, we establish that the proposed method\r\nis globally convergent for general functions provided that the line search satisfies theWolfe conditions. Numerical experiments are\r\nalso presented....
This paper presents an inverse problem and its solution procedure, which are aimed at identifying a sudden underwater movement of the sea bottom. The identification is mathematically shown to work with a known snapshot data of generated water wave configurations. It is also proved that the problem has a unique solution. However, the inverse problem is involved in an integral equation of the first kind, resulting in an ill-posed problem in the sense of stability. That is, the problem lacks solution stability properties. To overcome the difficulty of solution instability, in this paper, a stabilization technique, called regularization, is incorporated in the present solution procedure for the identification of the sea bottom movement. A numerical experiment is presented to demonstrate that the proposed (numerical) solution procedure operates....
In this paper, we propose an efficient numerical scheme for the approximate solution\nof a time fractional diffusion-wave equation with reaction term based on cubic\ntrigonometric basis functions. The time fractional derivative is approximated by the\nusual finite difference formulation, and the derivative in space is discretized using\ncubic trigonometric B-spline functions. A stability analysis of the scheme is conducted\nto confirm that the scheme does not amplify errors. Computational experiments are\nalso performed to further establish the accuracy and validity of the proposed scheme.\nThe results obtained are compared with finite difference schemes based on the\nHermite formula and radial basis functions. It is found that our numerical approach\nperforms superior to the existing methods due to its simple implementation,\nstraightforward interpolation and very low computational cost. A convergence\nanalysis of the scheme is also discussed....
A simulation was carried out on an unsteady flow of a viscous, incompressible and\nelectrically conducting fluid past an infinite vertical porous plate. A generic computer\nprogram using the Galerkin finite element method is employed to solve the\ncoupled non-linear differential equations for velocity and temperature fields. The\ndiffusion equation, the energy equation, the momentum equations and other relevant\nparameters are transformed into interpretable postfix codes. Numerical calculations\nare carried out on the flow fields both in the presence of cooling and heating of the\nplate by free convection currents. The effects of the dimensionless parameters,\nnamely, the Prandtl number, the Eckert number, the modified Grashof number, the\nSchmidt number and the time on the temperature and velocity distributions are discussed....
Item response theory (IRT) is a popular approach used for addressing large-scale statistical problems in psychometrics as well as in\nother fields. The fully Bayesian approach for estimating IRT models is usually memory and computationally expensive due to the\nlarge number of iterations. This limits the use of the procedure inmany applications. In an effort to overcome such restraint, previous\nstudies focused on utilizing the message passing interface (MPI) in a distributed memory-based Linux cluster to achieve certain\nspeedups. However, given the high data dependencies in a single Markov chain for IRT models, the communication overhead\nrapidly grows as the number of cluster nodes increases. This makes it difficult to further improve the performance under such\na parallel framework. This study aims to tackle the problem using massive core-based graphic processing units (GPU), which is\npractical, cost-effective, and convenient in actual applications.The performance comparisons among serial CPU, MPI, and compute\nunified device architecture (CUDA) programs demonstrate that the CUDA GPU approach has many advantages over the CPUbased\napproach and therefore is preferred....
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