Search results for: Navier- Stokes Equation

Authors: M. Hakak Khadem, M. Shams, S. Hossainpour

Abstract:

A two dimensional numerical simulation has been performed for incompressible and compressible fluid flow through microchannels in slip flow regime. The Navier-Stokes equations have been solved in conjunction with Maxwell slip conditions for modeling flow field associated with slip flow regime. The wall roughness is simulated with triangular microelements distributed on wall surfaces to study the effects of roughness on fluid flow. Various Mach and Knudsen numbers are used to investigate the effects of rarefaction as well as compressibility. It is found that rarefaction has more significant effect on flow field in microchannels with higher relative roughness. It is also found that compressibility has more significant effects on Poiseuille number when relative roughness increases. In addition, similar to incompressible models the increase in average fRe is more significant at low Knudsen number flows but the increase of Poiseuille number duo to relative roughness is sharper for compressible models. The numerical results have also validated with some available theoretical and experimental relations and good agreements have been seen.

Keywords: Relative roughness, slip flow, Poiseuille number.

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieh

Abstract:

In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: Polynomial constitutive equation, solitary.

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Authors: Chantawan Noisri, Robert Harold Buchanan Exell

Abstract:

A simple model for studying convectional lifting processes in the tropics is described in this paper with some tests of the model in dry air. The model consists of the density equation, the wind equation, the vertical velocity equation, and the temperature equation. The model domain is two-dimensional with length 100 km and height 17.5 km. Plan for experiments to investigate the effects of the heating surface, the deep convection approximation and the treatment of velocities at the boundaries are discussed. Equations for the simplified treatment of moisture in the atmosphere in future numerical experiments are also given.

Keywords: Numerical weather prediction, Finite differences, Convection lifting.

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Authors: Kyoungwoo Park, Ji-Won Han, Hyo-Jae Lim, Byeong-Sam Kim, Juhee Lee

Abstract:

Shape optimization of the airfoil with high aspect ratio of long endurance unmanned aerial vehicle (UAV) is performed by the multi-objective optimization technology coupled with computational fluid dynamics (CFD). For predicting the aerodynamic characteristics around the airfoil the high-fidelity Navier-Stokes solver is employed and SMOGA (Simple Multi-Objective Genetic Algorithm), which is developed by authors, is used for solving the multi-objective optimization problem. To obtain the optimal solutions of the design variable (i.e., sectional airfoil profile, wing taper ratio and sweep) for high performance of UAVs, both the lift and lift-to-drag ratio are maximized whereas the pitching moment should be minimized, simultaneously. It is found that the lift force and lift-to-drag ratio are linearly dependent and a unique and dominant solution are existed. However, a trade-off phenomenon is observed between the lift-to-drag ratio and pitching moment. As the result of optimization, sixty-five (65) non-dominated Pareto individuals at the cutting edge of design spaces that is decided by airfoil shapes can be obtained.

Keywords: Unmanned aerial vehicle (UAV), Airfoil, CFD, Shape optimization, Lift-to-drag ratio.

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Authors: G.Mehdiyeva, V.Ibrahimov, M.Imanova

Abstract:

As is known, one of the priority directions of research works of natural sciences is introduction of applied section of contemporary mathematics as approximate and numerical methods to solving integral equation into practice. We fare with the solving of integral equation while studying many phenomena of nature to whose numerically solving by the methods of quadrature are mainly applied. Taking into account some deficiency of methods of quadrature for finding the solution of integral equation some sciences suggested of the multistep methods with constant coefficients. Unlike these papers, here we consider application of hybrid methods to the numerical solution of Volterra integral equation. The efficiency of the suggested method is proved and a concrete method with accuracy order p = 4 is constructed. This method in more precise than the corresponding known methods.

Keywords: Volterra integral equation, hybrid methods, stability and degree, methods of quadrature

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Authors: A. Pérard Lecomte, G. Fokoua, A. Mehel, A. Tanière

Abstract:

Automotive experimental measurements in wind tunnel are often conducted on reduced scale. Depending on the study, different similitude parameters are used by researchers to best reproduce the flow at full scale. In this paper, two parameters are investigated, which are Reynolds number and upstream velocity when dealing with airflow of typical urban speed range, below 15 m.s-1. Their impact on flow structures and aerodynamic drag in the wake of a heavy truck model are explored. To achieve this, Computational Fluid Dynamics (CFD) simulations have been conducted with the aim of modeling the wake airflow of full- and reduced-scaled heavy trucks (1/4 and 1/28). The Reynolds Average Navier-Stokes (RANS) approach combined to the Reynolds Stress Model (RSM) as the turbulence model closure was used. Both drag coefficients and upstream velocity profiles (flow topology) were found to be close one another for the three investigated scales, when the dynamical similitude Reynolds is achieved. Moreover, the difference is weak for the simulations based on the same inlet air velocity. Hence, for the relative low velocity range investigated here, the impact of the scale factor is limited.

Keywords: Aerodynamics, CFD, heavy truck, recirculation area, scale effects, similitude parameters.

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Authors: Tanapat Brikshavana, Anirut Luadsong

Abstract:

The spectral action balance equation is an equation that used to simulate short-crested wind-generated waves in shallow water areas such as coastal regions and inland waters. This equation consists of two spatial dimensions, wave direction, and wave frequency which can be solved by finite difference method. When this equation with dominating propagation velocity terms are discretized using central differences, stability problems occur when the grid spacing is chosen too coarse. In this paper, we introduce the splitting modified donorcell scheme for avoiding stability problems and prove that it is consistent to the modified donor-cell scheme with same accuracy. The splitting modified donor-cell scheme was adopted to split the wave spectral action balance equation into four one-dimensional problems, which for each small problem obtains the independently tridiagonal linear systems. For each smaller system can be solved by direct or iterative methods at the same time which is very fast when performed by a multi-cores computer.

Keywords: donor-cell scheme, parallel algorithm, spectral action balance equation, splitting method.

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Authors: M. Nakisa, A. Maimun, Yasser M. Ahmed, F. Behrouzi, A. Tarmizi

Abstract:

The practical application of the Computational Fluid Dynamics (CFD), for predicting the flow pattern around Multipurpose Amphibious Vehicle (MAV) hull has made much progress over the last decade. Today, several of the CFD tools play an important role in the land and water going vehicle hull form design. CFD has been used for analysis of MAV hull resistance, sea-keeping, maneuvering and investigating its variation when changing the hull form due to varying its parameters, which represents a very important task in the principal and final design stages. Resistance analysis based on CFD (Computational Fluid Dynamics) simulation has become a decisive factor in the development of new, economically efficient and environmentally friendly hull forms. Three-dimensional finite volume method (FVM) based on Reynolds Averaged Navier-Stokes equations (RANS) has been used to simulate incompressible flow around three types of MAV hull bow models in steady-state condition. Finally, the flow structure and streamlines, friction and pressure resistance and velocity contours of each type of hull bow will be compared and discussed.

Keywords: RANS Simulation, Multipurpose Amphibious Vehicle, Viscous Flow Structure.

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Authors: Reza Abazari, Rasool Abazari

Abstract:

In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.

Keywords: Coupled Korteweg-de Vries(KdV) equation, Coupled Burgers equation, Coupled Schrödinger equation, differential transformation method.

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Authors: Carlos A. D. Torres, Antonio D. Delgado

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In this work we study the thermodynamic behavior of some ventilated facades under summer operating conditions in Southern Spain. Under these climatic conditions, indoor comfort implies a high energetic demand due to high temperatures that usually are reached in this season in the considered geographical area.

The aim of this work is to determine if during summer operating conditions in Southern Spain, ventilated façades provide some energy saving compared to the non-ventilated façades and to deduce their behavior patterns in terms of energy efficiency.

The modelization of the air flow in the channel has been performed by using Navier-Stokes equations for thermodynamic flows. Numerical simulations have been carried out with a 2D Finite Element approach.

This way, we analyze the behavior of ventilated façades under different weather conditions as variable wind, variable temperature and different levels of solar irradiation.

CFD computations show the combined effect of the shading of the external wall and the ventilation by the natural convection into the air gap achieve a reduction of the heat load during the summer period. This reduction has been evaluated by comparing the thermodynamic performances of two ventilated and two unventilated façades with the same geometry and thermophysical characteristics.

Keywords: Passive cooling, ventilated façades, energy-efficient building, CFD, FEM.

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Authors: Guohua Tu, Zhi Fu, Zhiwei Hu, Neil D Sandham, Jianqiang Chen

Abstract:

Tripping of boundary-layers from laminar to turbulent flow, which may be necessary in specific practical applications, requires high amplitude disturbances to be introduced into the boundary layers without large drag penalties. As a possible improvement on fixed trip devices, a technique based on vortex shedding for enhancing supersonic flow transition is demonstrated in the present paper for a Mach 1.5 boundary layer. The compressible Navier-Stokes equations are solved directly using a high-order (fifth-order in space and third-order in time) finite difference method for small-scale cylinders suspended transversely near the wall. For cylinders with proper diameter and mount location, asymmetry vortices shed within the boundary layer are capable of tripping laminar-turbulent transition. Full three-dimensional simulations showed that transition was enhanced. A parametric study of the size and mounting location of the cylinder is carried out to identify the most effective setup. It is also found that the vortex shedding can be suppressed by some factors such as wall effect.

Keywords: Boundary layer instability, boundary layer transition, vortex shedding, supersonic flows, flow control.

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Authors: Ahmet Tekcan

Abstract:

Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give some preliminaries from Pell equations x2 - dy2 = 1 and x2 - dy2 = N, where N be any fixed positive integer. In the second section, we consider the integer solutions of Pell equations x2 - dy2 = 1 and x2 - dy2 = 2t. We give a method for the solutions of these equations. Further we derive recurrence relations on the solutions of these equations

Keywords: Pell equation, solutions of Pell equation.

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Authors: Mohammad Taghi Darvishi, Mohammad Najafi

Abstract:

By means of the extended homoclinic test approach (shortly EHTA) with the aid of a symbolic computation system such as Maple, some complexiton type solutions for the (3+1)-dimensional Jimbo-Miwa equation are presented.

Keywords: Jimbo-Miwa equation, painleve analysis, Hirota's bilinear form, computerized symbolic computation.

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Authors: İnci M. Erhan

Abstract:

A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid.

Keywords: Bessel functions, Eigenfunction expansion, Quantum billiard, Schrödinger equation, Spherical harmonics

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Authors: M. A. Tayfun

Abstract:

Occurrences of spurious crests on the troughs of large, relatively steep second-order Stokes waves are anomalous and not an inherent characteristic of real waves. Here, the effects of such occurrences on the statistics described by the standard second-order stochastic model are examined theoretically and by way of simulations. Theoretical results and simulations indicate that when spurious occurrences are sufficiently large, the standard model leads to physically unrealistic surface features and inaccuracies in the statistics of various surface features, in particular, the troughs and thus zero-crossing heights of large waves. Whereas inaccuracies can be fairly noticeable for long-crested waves in both deep and shallower depths, they tend to become relatively insignificant in directional waves.

Keywords: Large waves, non-linear effects, simulation, spectra, spurious crests, Stokes waves, wave breaking, wave statistics.

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Authors: Felix Che Shu

Abstract:

We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study of the stability of such systems. This approach avoids requirement of the knowledge of the location of the characteristic roots of the equation with multiple delays which are generally more difficult to determine, compared to the location of the characteristic roots of equations with a single delay.

Keywords: Delay Differential Equation, Explicit Solution, Exponential Stability, Lyapunov Exponents, Multiple Delays.

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Authors: Masoud Abedini, Azrul A. Mutalib, Shahrizan Baharom, Hong Hao

Abstract:

This study was conducted published to investigate there liability of the equation pressure-impulse (PI) reinforced concrete column inprevious studies. Equation involves three different levels of damage criteria known as D =0. 2, D =0. 5 and D =0. 8.The damage criteria known as a minor when 0-0.2, 0.2-0.5is known as moderate damage, high damage known as 0.5-0.8, and 0.8-1 of the structure is considered a failure. In this study, two types of reliability analyzes conducted. First, using pressure-impulse equation with different parameters. The parameters involved are the concrete strength, depth, width, and height column, the ratio of longitudinal reinforcement and transverse reinforcement ratio. In the first analysis of the reliability of this new equation is derived to improve the previous equations. The second reliability analysis involves three types of columns used to derive the PI curve diagram using the derived equation to compare with the equation derived from other researchers and graph minimum standoff versus weapon yield Federal Emergency Management Agency (FEMA). The results showed that the derived equation is more accurate with FEMA standards than previous researchers.

Keywords: Blast load, RC column, P-I curve, Analytical formulae, Standard FEMA.

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Authors: M. Bayareh, S. Mortazavi

Abstract:

The migration of a deformable drop in simple shear flow at finite Reynolds numbers is investigated numerically by solving the full Navier-Stokes equations using a finite difference/front tracking method. The objectives of this study are to examine the effectiveness of the present approach to predict the migration of a drop in a shear flow and to investigate the behavior of the drop migration with different drop sizes and non-unity viscosity ratios. It is shown that the drop deformation depends strongly on the capillary number, so that; the proper non-dimensional number for the interfacial tension is the capillary number. The rate of migration increased with increasing the drop radius. In other words, the required time for drop migration to the centreline decreases. As the viscosity ratio increases, the drop rotates more slowly and the lubrication force becomes stronger. The increased lubrication force makes it easier for the drop to migrate to the centre of the channel. The migration velocity of the drop vanishes as the drop reaches the centreline under viscosity ratio of one and non-unity viscosity ratios. To validate the present calculations, some typical results are compared with available experimental and theoretical data.

Keywords: drop migration, shear flow, front-tracking method, finite difference method.

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Authors: Yan Su, Jane H. Davidson, F. A. Kulacki

Abstract:

The RANS method with Saffman-s turbulence model was employed to solve the time-dependent turbulent Navier-Stokes and energy equations for oscillating pipe flows. The method of partial sums of the Fourier series is used to analyze the harmonic velocity and temperature results. The complete structures of the oscillating pipe flows and the averaged Nusselt numbers on the tube wall are provided by numerical simulation over wide ranges of ReA and ReR. Present numerical code is validated by comparing the laminar flow results to analytic solutions and turbulence flow results to published experimental data at lower and higher Reynolds numbers respectively. The effects of ReA and ReR on the velocity, temperature and Nusselt number distributions have been di scussed. The enhancement of the heat transfer due to oscillating flows has also been presented. By the way of analyzing the overall Nusselt number over wide ranges of the Reynolds number Re and Keulegan- Carpenter number KC, the optimal ratio of the tube diameter over the oscillation amplitude is obtained based on the existence of a nearly constant optimal KC number. The potential application of the present results in sea water cooling has also been discussed.

Keywords: Keulegan-Carpenter number, Nusselt number, Oscillating pipe flows, Reynolds number

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Authors: Mohd Agos Salim Nasir, Ros Fadilah Deraman, Siti Salmah Yasiran

Abstract:

The Goursat partial differential equation arises in linear and non linear partial differential equations with mixed derivatives. This equation is a second order hyperbolic partial differential equation which occurs in various fields of study such as in engineering, physics, and applied mathematics. There are many approaches that have been suggested to approximate the solution of the Goursat partial differential equation. However, all of the suggested methods traditionally focused on numerical differentiation approaches including forward and central differences in deriving the scheme. An innovation has been done in deriving the Goursat partial differential equation scheme which involves numerical integration techniques. In this paper we have developed a new scheme to solve the Goursat partial differential equation based on the Adomian decomposition (ADM) and associated with Boole-s integration rule to approximate the integration terms. The new scheme can easily be applied to many linear and non linear Goursat partial differential equations and is capable to reduce the size of computational work. The accuracy of the results reveals the advantage of this new scheme over existing numerical method.

Keywords: Goursat problem, partial differential equation, Adomian decomposition method, Boole's integration rule.

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Authors: Ehsan Mahdavi

Abstract:

In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. Exp-function method is easy, succinct and powerful to implement to nonlinear partial differential equations arising in mathematical physics. We mainly try to present an application of Exp-function method and offer solutions for common errors wich occur during some of the recent works.

Keywords: Exp-function method, Rosenau Kawahara equation, Rosenau Korteweg-de Vries equation, nonlinear partial differential equation.

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Authors: H. Ozbasaran

Abstract:

IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.

Keywords: Cantilever, IPN, IPE, lateral torsional buckling

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Authors: Ali Pashaee, Parisa Shooshtari, Gholamreza Atae, Nasser Fatouraee

Abstract:

Phase-Contrast MR imaging methods are widely used for measurement of blood flow velocity components. Also there are some other tools such as CT and Ultrasound for velocity map detection in intravascular studies. These data are used in deriving flow characteristics. Some clinical applications are investigated which use pressure distribution in diagnosis of intravascular disorders such as vascular stenosis. In this paper an approach to the problem of measurement of intravascular pressure field by using velocity field obtained from flow images is proposed. The method presented in this paper uses an algorithm to calculate nonlinear equations of Navier- Stokes, assuming blood as an incompressible and Newtonian fluid. Flow images usually suffer the lack of spatial resolution. Our attempt is to consider the effect of spatial resolution on the pressure distribution estimated from this method. In order to achieve this aim, velocity map of a numerical phantom is derived at six different spatial resolutions. To determine the effects of vascular stenoses on pressure distribution, a stenotic phantom geometry is considered. A comparison between the pressure distribution obtained from the phantom and the pressure resulted from the algorithm is presented. In this regard we also compared the effects of collocated and staggered computational grids on the pressure distribution resulted from this algorithm.

Keywords: Flow imaging, pressure distribution estimation, phantom, resolution.

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Authors: Zdravka Aljinović, Snježana Pivac, Boško Šego

Abstract:

According to the interaction of inflation and unemployment, expectation of the rate of inflation in Croatia is estimated. The interaction between inflation and unemployment is shown by model based on three first-order differential i.e. difference equations: Phillips relation, adaptive expectations equation and monetary-policy equation. The resulting equation is second order differential i.e. difference equation which describes the time path of inflation. The data of the rate of inflation and the rate of unemployment are used for parameters estimation. On the basis of the estimated time paths, the stability and convergence analysis is done for the rate of inflation.

Keywords: Differencing, inflation, time path, unemployment.

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Authors: Tang Wei, Yang Xiaofeng, Gui Yewei, Du Yanxia

Abstract:

Complex lifting entry was selected for precise landing performance during the Mars Science Laboratory entry. This study aims to develop the three-dimensional numerical method for precise computation and the surface panel method for rapid engineering prediction. Detailed flow field analysis for Mars exploration mission was performed by carrying on a series of fully three-dimensional Navier-Stokes computations. The static aerodynamic performance was then discussed, including the surface pressure, lift and drag coefficient, lift-to-drag ratio with the numerical and engineering method. Computation results shown that the shock layer is thin because of lower effective specific heat ratio, and that calculated results from both methods agree well with each other, and is consistent with the reference data. Aerodynamic performance analysis shows that CG location determines trim characteristics and pitch stability, and certain radially and axially shift of the CG location can alter the capsule lifting entry performance, which is of vital significance for the aerodynamic configuration design and inner instrument layout of the Mars entry capsule.

Keywords: Mars entry capsule, static aerodynamics, computational fluid dynamics, hypersonic.

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Authors: Terrance Charles, Zhiyin Yang, Yiling Lu

Abstract:

Heavy trucks are aerodynamically inefficient due to their un-streamlined body shapes, leading to more than of 60% engine power being required to overcome the aerodynamics drag at 60 m/hr. There are many aerodynamics drag reduction devices developed and this paper presents a study on a drag reduction device called Cross Vortex Trap Device (CVTD) deployed in the gap between the tractor and the trailer of a simplified tractor-trailer model. Numerical simulations have been carried out at Reynolds number 0.51×10⁶ based on inlet flow velocity and height of the trailer using the Reynolds-Averaged Navier-Stokes (RANS) approach. Three different configurations of CVTD have been studied, ranging from single to three slabs, equally spaced on the front face of the trailer. Flow field around three different configurations of trap device have been analysed and presented. The results show that a maximum of 12.25% drag reduction can be achieved when a triple vortex trap device is used. Detailed flow field analysis along with pressure contours are presented to elucidate the drag reduction mechanisms of CVTD and why the triple vortex trap configuration produces the maximum drag reduction among the three configurations tested.

Keywords: Aerodynamic drag, cross vortex trap device, truck, RANS.

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Authors: N. Kumaresan , J. Kavikumar, Kuru Ratnavelu

Abstract:

In this paper, solution of fuzzy differential equation under general differentiability is obtained by simulink. The simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the simulink solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.

Keywords: Fuzzy differential equation, Generalized differentiability, H-difference and Simulink.

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Authors: F. Ekoue, A. Fouache d'Halloy, D. Gigon, G Plantamp, E. Zajdman

Abstract:

This work focuses on analysis of classical heat transfer equation regularized with Maxwell-Cattaneo transfer law. Computer simulations are performed in MATLAB environment. Numerical experiments are first developed on classical Fourier equation, then Maxwell-Cattaneo law is considered. Corresponding equation is regularized with a balancing diffusion term to stabilize discretizing scheme with adjusted time and space numerical steps. Several cases including a convective term in model equations are discussed, and results are given. It is shown that limiting conditions on regularizing parameters have to be satisfied in convective case for Maxwell-Cattaneo regularization to give physically acceptable solutions. In all valid cases, uniform convergence to solution of initial heat equation with Fourier law is observed, even in nonlinear case.

Keywords: Maxwell-Cattaneo heat transfers equations, fourierlaw, heat conduction, numerical solution.

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Authors: Mahdi Nouri

Abstract:

In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.

Keywords: Riccati, matrix equation, eigenvalue problem, symmetric, bisymmetric, persymmetric, decomposition, canonical forms, Graphs theory, adjacency and Laplacian matrices.

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Authors: Tian Baoguang, Liang Chunyan, Chen Nan

Abstract:

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δ_i are discussed. An algorithm that avoids matrix inversion with the case -1<-δ_i<0 is proposed.

Keywords: Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion

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