Search results for: numerical approximation schemes

Authors: Zafar Iqbal Zafar, Abdul Waheed

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The Capital Development Authority (CDA) Ordinance 1960 requires CDA to acquire land for the provision of housing in Islamabad. However, the pace of residential development was slow and the demand for housing was increasing rapidly. To resolve the growing housing problem, CDA involved the private sector in the development of housing schemes. Detailed bye-laws for regulation of private housing schemes were prepared and these bylaws were called “Modalities & Procedures”. This paper explains how the Modalities and Procedures of CDA have been successful in regulating the development of private housing schemes in Islamabad.

Keywords: housing schemes, master plan, development works, zoning regulations

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Norhashidah Hj Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two-dimensional Helmholtz equation. The formulation is based on the nine-point fourth-order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula

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Authors: Cletus Abhulimen, L. A. Ukpebor

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In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.

Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations

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Authors: Ali Yasin, Ali Kamran, Muhammad Safdar

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In order to reduce the hefty cost involved in terms of time and project cost, the development and application of advanced numerical tools to address the burn-back analysis problem in solid rocket motor design and development is the need of time. Several advanced numerical schemes have been developed in recent times, but their usage in the design of propellant grain of solid rocket motors is very rare. In this paper, an advanced numerical technique named the Level-Set method has been utilized for the burn-back analysis of star grain to study the effect of geometrical parameters on ballistic performance indicators such as solid loading, neutrality, and sliver percentage. In the level set technique, simple finite difference methods may fail quickly and require more sophisticated non-oscillatory schemes for feasible long-time simulation. For internal ballistic calculations, a simplified equilibrium pressure method is utilized. Preliminary results of the operative conditions, for all the combustion time, of star grain burn-back using level set techniques are compared with published results using CAD technique to test the developed numerical model.

Keywords: solid rocket motor, internal ballistic, level-set technique, star grain

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Authors: Tirtha Raj Dhakal, Brian Davidson, Bob Farquharson

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Institutional design is an important aspect in efficient water resource management. In Nepal, the water supply in both farmers’- and agency-managed irrigation systems has become sub-standard because of the weak institutional framework. This study characterizes both forms of the schemes and links existing institution and governance of the schemes with its performance with reference to cost recovery, maintenance of the schemes and water distribution throughout the schemes. For this, two types of surveys were conducted. A management survey of ten farmers’-managed and five agency-managed schemes of Chitwan valley and its periphery was done. Also, a farm survey comprising 25 farmers from each of head, middle and tail regions of both schemes; Narayani Lift Irrigation Project (agency-managed) and Khageri Irrigation System (farmers’-managed) of Chitwan Valley as a case study was conducted. The results showed that cost recovery of agency-managed schemes in 2015 was less than two percent whereas service fee collection rate in farmers’-managed schemes was nearly 2/3rd that triggered poor maintenance of the schemes and unequal distribution of water throughout the schemes. Also, the institution on practice is unable to create any incentives for farmers for economical use of water as well as willingness to pay for its use. This, thus, compels the need of refined institutional framework which has been suggested in this paper aiming to improve the cost recovery and better water distribution throughout the irrigation schemes.

Keywords: cost recovery, governance, institution, schemes' performance

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Authors: Yu Liang, Wei Wei

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Spatial representation of numbers and numerical magnitude are important for preschoolers’ mathematical ability. Mental number line, a typical index to measure numbers spatial representation, and numerical comparison are both related to arithmetic obviously. However, they seem to rely on different mechanisms and probably influence arithmetic through different mechanisms. In line with this idea, preschool children were trained with two tasks to investigate which one is more important for approximate arithmetic. The training of numerical processing and number line estimation were proved to be effective. They both improved the ability of approximate arithmetic. When the difficulty of approximate arithmetic was taken into account, the performance in number line training group was not significantly different among three levels. However, two harder levels achieved significance in numerical comparison training group. Thus, comparing spatial representation ability, symbolic approximation arithmetic relies more on numerical magnitude. Educational implications of the study were discussed.

Keywords: approximate arithmetic, mental number line, numerical magnitude, preschooler

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Authors: Chaghoub Soraya, Zhang Xiaoyan

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This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques.

Keywords: approximation algorithms, buy-at-bulk, combinatorial optimization, network design, p-median

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Authors: Mounir Adal, Baalal Azeddine, Afifi Moulay Larbi

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Numerical analysis is a branch of mathematics devoted to the development of iterative matrix calculation techniques. We are searching for operations optimization as objective to calculate and solve systems of equations of order n with time and energy saving for computers that are conducted to calculate and analyze big data by solving matrix equations. Furthermore, this scientific discipline is producing results with a margin of error of approximation called rates. Thus, the results obtained from the numerical analysis techniques that are held on computer software such as MATLAB or Simulink offers a preliminary diagnosis of the situation of the environment or space targets. By this we can offer technical procedures needed for engineering or scientific studies exploitable by engineers for water.

Keywords: numerical analysis methods, obstacles solving, engineering, simulation, numerical modeling, iteration, computer, MATLAB, water, underground, velocity

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Authors: Keunhong Chae, Seokho Yoon

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In this paper, frequency offset (FO) estimation schemes robust to the non-Gaussian noise environments are proposed for orthogonal frequency division multiplexing (OFDM) systems. First, a maximum-likelihood (ML) estimation scheme in non-Gaussian noise environments is proposed, and then, the complexity of the ML estimation scheme is reduced by employing a reduced set of candidate values. In numerical results, it is demonstrated that the proposed schemes provide a significant performance improvement over the conventional estimation scheme in non-Gaussian noise environments while maintaining the performance similar to the estimation performance in Gaussian noise environments.

Keywords: frequency offset estimation, maximum-likelihood, non-Gaussian noise environment, OFDM, training symbol

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

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In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: explicit group method, finite difference, helmholtz equation, rotated grid, standard grid

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Authors: Khaled Moaddy

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In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: standard finite difference schemes, non-standard schemes, Laplace equation, Dirichlet boundary conditions

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Authors: Smita Sonker, Uaday Singh

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Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries.

Keywords: Lipschitz classes, product matrix operator, signals, trigonometric Fourier approximation

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Authors: Gregor Kosec

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Simple and robust numerical approach for solving flow problems is presented, where involved physical fields are represented through the local approximation functions, i.e., the considered field is approximated over a local support domain. The approximation functions are then used to evaluate the partial differential operators. The type of approximation, the size of support domain, and the type and number of basis function can be general. The solution procedure is formulated completely through local computational operations. Besides local numerical method also the pressure velocity is performed locally with retaining the correct temporal transient. The complete locality of the introduced numerical scheme has several beneficial effects. One of the most attractive is the simplicity since it could be understood as a generalized Finite Differences Method, however, much more powerful. Presented methodology offers many possibilities for treating challenging cases, e.g. nodal adaptivity to address regions with sharp discontinuities or p-adaptivity to treat obscure anomalies in physical field. The stability versus computation complexity and accuracy can be regulated by changing number of support nodes, etc. All these features can be controlled on the fly during the simulation. The presented methodology is relatively simple to understand and implement, which makes it potentially powerful tool for engineering simulations. Besides simplicity and straightforward implementation, there are many opportunities to fully exploit modern computer architectures through different parallel computing strategies. The performance of the method is presented on the lid driven cavity problem, backward facing step problem, de Vahl Davis natural convection test, extended also to low Prandtl fluid and Darcy porous flow. Results are presented in terms of velocity profiles, convergence plots, and stability analyses. Results of all cases are also compared against published data.

Keywords: fluid flow, meshless, low Pr problem, natural convection

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Authors: Archit Yajnik, Rustam Ali

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In this paper, numerical method based on discrete GHM multiwavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete GHM multiwavelet. A number of examples are demonstrated to justify the applicability of the method. In GHM multiwavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient as compared to quadrature method.

Keywords: GHM multiwavelet, fredholm integral equations, quadrature method, function approximation

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Authors: Anusuya Ghosh, Vishnu Narayanan

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The approximation of convex set by semidefinite representable set plays an important role in semidefinite programming, especially in modern convex optimization. To optimize a linear function over a convex set is a hard problem. But optimizing the linear function over the semidefinite representable set which approximates the convex set is easy to solve as there exists numerous efficient algorithms to solve semidefinite programming problems. So, our approximation technique is significant in optimization. We develop a technique to approximate any closed convex set, say K by compactly semidefinite representable set. Further we prove that there exists a sequence of compactly semidefinite representable sets which give tighter approximation of the closed convex set, K gradually. We discuss about the convergence of the sequence of compactly semidefinite representable sets to closed convex set K. The recession cone of K and the recession cone of the compactly semidefinite representable set are equal. So, we say that the sequence of compactly semidefinite representable sets converge strongly to the closed convex set. Thus, this approximation technique is very useful development in semidefinite programming.

Keywords: semidefinite programming, semidefinite representable set, compactly semidefinite representable set, approximation

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Authors: Tulin Coskun

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We investigate the approximation of analytic functions of several variables in polydisc by the sequences of linear k-positive operators in Gadjiev sence. The approximation of analytic functions of complex variable by linear k-positive operators was tackled, and k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc were introduced in the past. Recently, very general results on convergence of the sequences of linear k-positive operators on a simply connected bounded domain within the space of analytic functions were proved. In this presentation, we extend some of these results to the approximation of analytic functions of several complex variables by sequences of linear k-positive operators.

Keywords: analytic functions, approximation of analytic functions, Linear k-positive operators, Korovkin type theorems

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Authors: Fatema-Tuz-Zahura, Raquib Ahsan

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Punching shear failure is usually the governing failure mode of flat plate structures. Punching failure is brittle in nature which induces more vulnerability to this type of structure. In the present study, a 3D finite element model of a flat plate with low reinforcement ratio and without any transverse reinforcement has been developed. Punching shear stress and the deflection data were obtained on the surface of the flat plate as well as through the thickness of the model from numerical simulations. The obtained data were compared with the experimental results. Variation of punching stress with respect to deflection as obtained from numerical results is found to be in good agreement with the experimental results; the range of variation of punching stress is within 5%. The numerical simulation shows an early and gradual onset of nonlinearity, whereas the same is late and abrupt as observed in the experimental results. The range of variation of punching stress for different slab thicknesses between experimental and numerical results is less than 15%. The developed numerical model is useful to complement available punching test series performed in the past. The results obtained from the numerical model will be helpful for designing retrofitting schemes of flat plates.

Keywords: flat plate, finite element model, punching shear, reinforcement ratio

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Authors: Hare Krishna Nigam

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In this paper, for the first time, (E,q)(C,2) product summability method is introduced and two quite new results on degree of approximation of the function f belonging to Lip (alpha,r)class and W(L(r), xi(t)) class by (E,q)(C,2) product means of Fourier series, has been obtained.

Keywords: Degree of approximation, (E, q)(C, 2) means, Fourier series, Lebesgue integral, Lip (alpha, r)class, W(L(r), xi(t))class of functions

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Authors: Kairat T. Mynbaev, Elena N. Lomakina

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We consider a Hardy-type operator generated by a family of open subsets of a Hausdorff topological space. The family is indexed with non-negative real numbers and is totally ordered. For this operator, we obtain two-sided bounds of its norm, a compactness criterion, and bounds for its approximation numbers. Previously, bounds for its approximation numbers have been established only in the one-dimensional case, while we do not impose any restrictions on the dimension of the Hausdorff space. The bounds for the norm and conditions for compactness earlier have been found using different methods by G. Sinnamon and K. Mynbaev. Our approach is different in that we use domain partitions for all problems under consideration.

Keywords: approximation numbers, boundedness and compactness, multidimensional Hardy operator, Hausdorff topological space

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Authors: Qiming Zhang, Youda Ye, Qinxue Jiang

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Accurate prediction of external flowfield and aero-heating at the wall of hypersonic vehicle is very crucial for the design of aircrafts. Unstructured/hybrid meshes have more powerful advantages than structured meshes in terms of pre-processing, parallel computing and mesh adaptation, so it is imperative to develop high-resolution numerical methods for the calculation of aerothermal environment on unstructured/hybrid meshes. The inviscid flux scheme is one of the most important factors affecting the accuracy of unstructured/ hybrid mesh heat flux calculation. Here, a new hybrid flux scheme is developed and the approach of interface type selection is proposed: i.e. 1) using the exact Riemann scheme solution to calculate the flux on the faces parallel to the wall; 2) employing Sterger-Warming (S-W) scheme to improve the stability of the numerical scheme in other interfaces. The results of the heat flux fit the one observed experimentally and have little dependence on grids, which show great application prospect in unstructured/ hybrid mesh.

Keywords: aero-heating prediction, computational fluid dynamics, hybrid meshes, hybrid schemes

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Authors: A. M. Sagir

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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: Marian Sagat, Mariana Remesikova

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In civil engineering, there is a problem how to industrially produce tensile membrane structures that are non-developable surfaces. Nondevelopable surfaces can only be developed with a certain error and we want to minimize this error. To that goal, the non-developable surfaces are cut into plates along to the geodesic curves. We propose a numerical algorithm for finding approximations of open geodesics on meshes and surfaces based on geodesic curvature flow. For practical reasons, it is important to automatize the choice of the time step. We propose a method for automatic setting of the time step based on the diagonal dominance criterion for the matrix of the linear system obtained by discretization of our partial differential equation model. Practical experiments show reliability of this method. Because approximation of the model is made by numerical method based on classic derivatives, it is necessary to solve obstacles which occur for meshes with sharp corners. We solve this problem for big family of meshes with sharp corners via special rotations which can be seen as partial unfolding of the mesh. In practical applications, it is required that the approximation of geodesic has its vertices only on the edges of the mesh. This problem is solved by a specially designed pointing tracking algorithm. We also partially solve the problem of finding geodesics on meshes with holes. We implemented the whole algorithm in Rhinoceros (commercial 3D computer graphics and computer-aided design software ). It is done by using C# language as C# assembly library for Grasshopper, which is plugin in Rhinoceros.

Keywords: geodesic, geodesic curvature flow, mesh, Rhinoceros software

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Authors: Kejal Khatri, Vishnu Narayan Mishra

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We compute the degree of approximation of functions\tilde{f}\in H_w, a new Banach space using (T.E^1) summability means of conjugate Fourier series. In this paper, we extend the results of Singh and Mahajan which in turn generalizes the result of Lal and Yadav. Some corollaries have also been deduced from our main theorem and particular cases.

Keywords: conjugate Fourier series, degree of approximation, Hölder metric, matrix summability, product summability

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Authors: Mohd Zuhair, Ram Babu Roy

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This paper presents an overview of the accessibility, design, and functioning of health insurance plans launched by state governments in India. In recent years, the governments of several states in India have come forward to provide health insurance coverage for the low-income group and rural population to reduce the out of pocket expenditure (OPE) on healthcare. Different health insurance schemes have different structures and offerings which differ in the different demographic factors. This study will portray a comparative analysis of the various health insurance schemes by analyzing different offerings and finance generation of the schemes. The comparative analysis will explain the lesson to be learned from these schemes and extend the existing knowledge of the health insurance in India. This would help in recognizing tension between various drivers and identifying issues pertaining to the sustainability of health insurance schemes in India.

Keywords: health insurance, out of pocket expenditure, universal healthcare, sustainability

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Authors: Raphael de Oliveira Garcia, Samuel Rocha de Oliveira

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We have developed a new computer program in Fortran 90, in order to obtain numerical solutions of a system of Relativistic Magnetohydrodynamics partial differential equations with predetermined gravitation (GRMHD), capable of simulating the formation of relativistic jets from the accretion disk of matter up to his ejection. Initially we carried out a study on numerical methods of unidimensional Finite Volume, namely Lax-Friedrichs, Lax-Wendroff, Nessyahu-Tadmor method and Godunov methods dependent on Riemann problems, applied to equations Euler in order to verify their main features and make comparisons among those methods. It was then implemented the method of Finite Volume Centered of Nessyahu-Tadmor, a numerical schemes that has a formulation free and without dimensional separation of Riemann problem solvers, even in two or more spatial dimensions, at this point, already applied in equations GRMHD. Finally, the Nessyahu-Tadmor method was possible to obtain stable numerical solutions - without spurious oscillations or excessive dissipation - from the magnetized accretion disk process in rotation with respect to a central black hole (BH) Schwarzschild and immersed in a magnetosphere, for the ejection of matter in the form of jet over a distance of fourteen times the radius of the BH, a record in terms of astrophysical simulation of this kind. Also in our simulations, we managed to get substructures jets. A great advantage obtained was that, with the our code, we got simulate GRMHD equations in a simple personal computer.

Keywords: finite volume methods, central schemes, fortran 90, relativistic astrophysics, jet

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Authors: Farouk Metiri, Halim Zeghdoudi, Mohamed Riad Remita

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Credibility theory is an experience rating technique in actuarial science which can be seen as one of quantitative tools that allows the insurers to perform experience rating, that is, to adjust future premiums based on past experiences. It is used usually in automobile insurance, worker's compensation premium, and IBNR (incurred but not reported claims to the insurer) where credibility theory can be used to estimate the claim size amount. In this study, we focused on a popular tool in credibility theory which is the Bayesian premium estimator, considering Lindley distribution as a claim distribution. We derive this estimator under entropy loss which is asymmetric and squared error loss which is a symmetric loss function with informative and non-informative priors. In a purely Bayesian setting, the prior distribution represents the insurer’s prior belief about the insured’s risk level after collection of the insured’s data at the end of the period. However, the explicit form of the Bayesian premium in the case when the prior is not a member of the exponential family could be quite difficult to obtain as it involves a number of integrations which are not analytically solvable. The paper finds a solution to this problem by deriving this estimator using numerical approximation (Lindley approximation) which is one of the suitable approximation methods for solving such problems, it approaches the ratio of the integrals as a whole and produces a single numerical result. Simulation study using Monte Carlo method is then performed to evaluate this estimator and mean squared error technique is made to compare the Bayesian premium estimator under the above loss functions.

Keywords: bayesian estimator, credibility theory, entropy loss, monte carlo simulation

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Authors: M. Y. Waziri, M. A. Aliyu

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The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

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Authors: Luke Ukpebor, C. E. Abhulimen

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Stiff initial value problems in ordinary differential equations are problems for which a typical solution is rapidly decaying exponentially, and their numerical investigations are very tedious. Conventional numerical integration solvers cannot cope effectively with stiff problems as they lack adequate stability characteristics. In this article, we developed a new family of four-step second derivative exponentially fitted method of order six for the numerical integration of stiff initial value problem of general first order differential equations. In deriving our method, we employed the idea of breaking down the general multi-derivative multistep method into predator and corrector schemes which possess free parameters that allow for automatic fitting into exponential functions. The stability analysis of the method was discussed and the method was implemented with numerical examples. The result shows that the method is A-stable and competes favorably with existing methods in terms of efficiency and accuracy.

Keywords: A-stable, exponentially fitted, four step, predator-corrector, second derivative, stiff initial value problems

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Authors: Najwa Mimouni, Omar Rahli, Rachid Bennacer, Salah Chikh

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In the present work 2D and 3D numerical simulations of double diffusion natural convection in an elongated enclosure filled with a binary fluid saturating a porous medium are carried out. In the formulation of the problem, the Boussinesq approximation is considered and cross Neumann boundary conditions are specified for heat and mass walls conditions. The numerical method is based on the control volume approach with the third order QUICK scheme. Full approximation storage (FAS) with full multigrid (FMG) method is used to solve the problem. For the explored large range of the controlling parameters, we clearly evidenced that the increase in the depth of the cavity i.e. the lateral aspect ratio has an important effect on the flow patterns. The 2D perfect parallel flows obtained for a small lateral aspect ratio are drastically destabilized by increasing the cavity lateral dimension. This yields a 3D fluid motion with a much more complicated flow pattern and the classically studied 2D parallel flows are impossible.

Keywords: bifurcation, natural convection, heat and mass transfer, parallel flow, porous media

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