an implicit fourth order compact finite difference scheme for one dimensional burgers equation abstract a fourth order compact finite difference method is proposed in this paper to solve one dimensional burgers equation the newly proposed method is based on the hopf cole transformation which transforms the original nonlinear burgers equation into a linear heat equation and transforms the dirichlet boundary condition into the robin boundary condition the linear heat equation is then solved by an implicit fourth order compact finite difference scheme a compact fourth order formula is also developed to approximate the robin boundary conditions while the initial condition for the heat equation is approximated using simpson s rule to maintain overall fourth order accuracy numerical experiments have been conducted to demonstrate the efficiency and high order accuracy of this method the numerical results also show that the method is unconditionally stable as there is no constraint on time step size

numerical solutions of the modified burgers equation by petrov galerkin method abstract the modified burgers equation mbe is solved numerically by the petrov galerkin method using a linear hat function as the trial function and a cubic b spline function as the test function product approximation has been used in this method a linear stability analysis of the scheme shows it to be unconditionally stable the accuracy of the presented method is demonstrated by two test problems the numerical results are found in good agreement with the exact solutions

new algorithms for euclidean distance transformation of an n dimensional digitized picture with applications abstract in this paper we propose a new method to obtain the euclidean distance transformation and the voronoi diagram based on the exact euclidean metric for an n dimensional picture we present four algorithms to perform the transformation which are constructed by the serial composition of n dimensional filters when performed by a general purpose computer they are faster than the method by h yamada for a two dimensional picture those algorithms require only one n dimensional array for storing input output pictures and a single one dimensional array for a work area if an input picture needs not be preserved

permanence extinction and global asymptotic stability in a stage structured system with distributed delays in this paper we consider a nonautonomous stage structured competitive system of n species population growth with distributed delays which takes into account the delayed feedback in both interspecific and intraspecific interactions we obtain by using the method of repeated replace sufficient conditions for permanence and extinction of the species the global attractivity of the unique positive equilibrium is proved in the autonomous case our results extend previous ones obtained by liu et al in nonlinear anal 51 2002 1347 1361 j math anal appl 274 2002 667 684

a parameter uniform implicit difference scheme for solving time dependent burgers equations abstract a numerical study is made for solving one dimensional time dependent burgers equation with small coefficient of viscosity burgers equation is one of the fundamental model equations in the fluid dynamics to describe the shock waves and traffic flows for high coefficient of viscosity a number of solution methodology exist in the literature 6 7 8 9 and 14 but for the sufficiently low coefficient of viscosity the exist solution methodology fail and a discrepancy occurs in the literature in this paper we present a numerical method based on finite difference which works nicely for both the cases i e low as well as high viscosity coefficient the method comprises a standard implicit finite difference scheme to discretize in temporal direction on uniform mesh and a standard upwind finite difference scheme to discretize in spacial direction on piecewise uniform mesh the quasilinearzation process is used to tackle the non linearity an extensive amount of analysis has been carried out to obtain the parameter uniform error estimates which show that the resulting method is uniformly convergent with respect to the parameter to illustrate the method numerical examples are solved using the presented method and compare with exact solution for high value of coefficient of viscosity

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

explicit solutions of nonlinear partial differential equations explicit solutions are calculated by the decomposition method for burger s equation for comparison with other existing procedures such as similarity reduction etc

competitive systems with stage structure of distributed delay type this paper considers a delay differential equation model for the interaction among n species the adult members of which are in competition for each of the n species the model incorporates an infinite distributed time delay which represents the time from birth to maturity of that species thus the time delays appear in the adult recruitment terms the dynamics of the model are determined and sharp global stability criteria are established for the interior equilibrium as well as the axial equilibrium

a structure preserving bhattacharya method for nonlinear parabolic equations with fractional diffusion and advection abstract in this work we investigate a parabolic equation with nonlinear reaction and fractional diffusion and advection terms of the riesz type the model under investigation is a fractional generalization of the well known burgers fisher and burgers huxley models from population and fluid dynamics which are equations that admit positive bounded and monotone solutions some of them being traveling waves a variable step bhattacharya type finite difference scheme based on fractional centered differences is proposed to approximate the solutions of the parabolic partial differential equation the method is an explicit technique which under suitable parameter conditions is capable of preserving the positivity the boundedness and the monotonicity of the approximations moreover the method preserves the constant solutions of the fractional partial differential equation under investigation the properties of consistency stability and convergence of the technique are established thoroughly in this manuscript along with some a priori bounds for the numerical solutions some illustrative simulations and numerical comparisons against other numerical techniques are carried out in order to show that the method preserves these features of the approximations

numerical detection of instability regions for delay models with delay dependent parameters in this paper we are interested in gaining local stability insights about the interior equilibria of delay models arising in biomathematics the models share the property that the corresponding characteristic equations involve delay dependent coefficients the presence of such dependence requires the use of suitable criteria which usually makes the analytical work harder so that numerical techniques must be used most existing methods for studying stability switching of equilibria fail when applied to such a class of delay models to this aim an efficient criterion for stability switches was recently introduced in e beretta y kuang geometric stability switch criteria in delay differential systems with delay dependent parameters siam j math anal 33 2002 1144 1165 and extended e beretta y tang extension of a geometric stability switch criterion funkcial ekvac 46 3 2003 337 361 we describe how to numerically detect the instability regions of positive equilibria by using such a criterion considering both discrete and distributed delay models

efficient numerical techniques for burgers equation this paper presents new efficient numerical techniques for solving one dimensional quasi linear burgers equation burgers equation is used as a model problem in the study of turbulence boundary layer behavior shock waves convection dominated diffusion phenomena gas dynamics acoustic attenuation in fog and continuum traffic simulation using a non linear cole hopf transformation the burgers equation is reduced to one dimensional diffusion equation the linearized diffusion equation is semi discretized by using method of lines mol which leads to a system of ordinary differential equations in time resulting system of ordinary differential equations is solved by backward differentiation formulas bdf of order one two and three and the analysis of numerical errors are presented numerical results for modest values of kinematic viscosity are compared with the exact solution to demonstrate the efficiency of proposed numerical methods

a computational method for solving one dimensional variable coefficient burgers equation abstract the burgers equation is a simple one dimensional model of the navier stoke equation in this paper the exact solution to one dimensional variable coefficient burgers equation is obtained in the reproducing kernel space w 2 3 the exact solution is represented in the form of series the n term approximation u n t x to exact solution u t x is proved to converge to the exact solution moreover the approximate error of u n t x is monotone decreasing some numerical examples have been studied to demonstrate the accuracy of the present method results obtained by the method have been compared with the exact solution of each example and are found to be in good agreement with each other

a finite element approach for solution of burgers equation in this study for the burgers equation which is used a model problem in turbulence and shock wave theory was given a finite element solution considering the numerical results obtained for different values of viscosity compared with cole s analytical solution it was seen that they were in good agreement

error analysis of approximate solutions of non linear burgers equation this paper deals with application of the maximum principle for differential equations to the finite difference method for determining upper and lower approximate solutions of the non linear burgers equation and their error range in term of mathematical architecture the paper is based on the maximum principle for parabolic differential equations to establish monotonic residual relations of the burgers equation and in terms of numerical method it applies the finite difference method to discretize the equation followed by use of the proposed residual correction method for obtaining its optimal solutions under constraint conditions for inequalities derived by using this approach the upper and lower transient approximate solutions are not just useful in analyzing the range of the maximum possible error between them and the analytic solutions correctly and the numerical validations also indicate good accuracy in mean values of the upper and lower approximate solutions

numerical solution of burgers equation by quadratic b spline finite elements in this paper a galerkin quadratic b spline finite element method is used to solve numerically the one dimensional burgers equation reduced by the hopf cole transformation the performance of the method is tested on two model problems involving moderately reynolds numbers with known exact solutions the obtained numerical results show that the method is efficient robust and reliable for solving burgers equation accurately even involving high reynolds numbers for which the exact solution fails computed results are compared with other numerical results in the literature a stability analysis of the method is also investigated

an efficient numerical scheme for burgers equation this paper applies the multiquadric mq as a spatial approximation scheme for solving the nonlinear burgers equation for comparison purposes a low order explicit finite difference approximation of the time derivative is employed by decreasing the time step of the computation it is shown that the major numerical error is from the time integration instead of the mq spatial approximation the numerical results indicate that this mq offers an excellent approximation for all possible values of reynolds number an adaptive algorithm is also developed to adjust the mq interpolation points to the peak of the shock wave which is shown to provide an improved numerical result numerical comparisons are made with most of the existing numerical schemes for solving the burgers equation

the semi approximate approach for solving burgers equation with high reynolds number this paper presents the solution of burgers equation involving very high reynolds number re 5 we use semi implicit time difference scheme to reduce burgers equation to two point non linear ordinary differential equation and solved it by matched asymptotic expansion method

numerical solution of one dimensional burgers equation using reproducing kernel function this paper presents a numerical method for one dimensional burgers equation by the hopf cole transformation and a reproducing kernel function abbreviated as rkf the numerical solution is given as explicit integral expressions with the rkf at each time step so that the computation is fully parallel the stability and error estimates are derived numerical results for some test problems are presented and compared with the exact solutions some numerical results are also compared with the results obtained by other methods the present method is easily implemented and effective

a predictor corrector compact finite difference scheme for burgers equation abstract in this paper a compact predictor corrector finite difference scheme is proposed to solve the burgers equation the scheme is based on compact derivatives approximation by which we get the spatial approximations of first order derivatives and second order derivatives with fourth order accuracy both for inner nodes and boundary nodes for the first time derivative item a two step predictor corrector method called maccormack method is used numerical experiments show the scheme is in good agreement with the exact solutions

biorthogonal multiwavelets on the interval for numerical solutions of burgers equation to numerically solve the burgers equation in this paper we propose a general method for constructing wavelet bases on the interval 0 1 derived from symmetric biorthogonal multiwavelets on the real line in particular we obtain wavelet bases with simple structures on the interval 0 1 from the hermite cubic splines in comparison with all other known constructed wavelets on the interval 0 1 our constructed wavelet bases on the interval 0 1 from the hermite cubic splines not only have good approximation and symmetry properties with extremely short supports but also employ a minimum number of boundary wavelets with a very simple structure these desirable properties make them to be of particular interest in numerical algorithms our constructed wavelet bases on the interval 0 1 are then used to solve the nonlinear burgers equation our method is based on the finite difference formula combined with the collocation method therefore our proposed numerical scheme in this paper is abbreviated as mfdcm mixed finite difference and collocation method some numerical examples are provided to demonstrate the validity and applicability of our proposed method which can be easily implemented to produce a desired accuracy

the asymptotic behaviors of a stage structured autonomous predator prey system with time delay abstract in this paper we consider an autonomous predator prey lotka volterra system in which individuals in the population may belong to one of two classes the immatures and the matures the age to maturity is represented by a time delay by using eigenvalue analysis principal term analyze method reduction to absurdity and iterative method we obtain some simple conditions for global asymptotic stability of the unique positive equilibrium point moreover a condition that the prey population in the system get extinction and the predator population in the system get permanence will be obtained meanwhile the theorems extend the corresponding conclusions in which there have no two stage structures

global analysis of the predator prey system with beddington deangelis functional response abstract in this paper predator prey systems with beddington deangelis functional response are considered by using divergency criterion global stability is established provided the system possesses a positive locally asymptotically stable equilibrium

an efficient robust numerical method for singularly perturbed burgers equation abstract in this article we propose a parameter uniformly convergent numerical method for viscous burgers equation in order to find a numerical approximation to burgers equation we linearize the equation to obtain sequence of linear pdes the linear pdes are solved by a finite difference scheme which comprises of the backward difference scheme for the time derivative and upwind finite difference scheme for the spatial derivatives layer adapted nonuniform meshes are invoked at each time level to exhibit layer nature of the solution the nonuniform meshes are obtained by equidistribution of a positive integrable monitor function which involves the derivative of the solution it is shown that the methods converges uniformly with respect to the perturbation parameter numerical experiments are carried out to validate the e uniform error estimate of o n 1 t

on the dynamics of predator prey models with the beddington deangelis functional response abstract the dynamics of predator prey models with the beddington deangelis functional response are analyzed primarily from the viewpoint of permanence uniform persistence the beddington deangelis functional response is similar to the holling type 2 functional response but contains an extra term describing mutual interference by predators both spatially homogeneous models based on ordinary differential equations and reaction diffusion models are considered criteria for permanence and for predator extinction are derived for systems without diffusion or with no flux boundary conditions criteria are derived for the existence of a globally stable coexistence equilibrium or alternatively for the existence of periodic orbits

fourth order finite difference method for solving burgers equation abstract in this paper we present fourth order finite difference method for solving nonlinear one dimensional burgers equation this method is unconditionally stable the convergence analysis of the present method is studied and an upper bound for the error is derived numerical comparisons are made with most of the existing numerical methods for solving this equation

an accurate approximation algorithm for burgers equation in the presence of small viscosity abstract most of the existing numerical schemes developed to solve burgers equation cannot exhibit its correct physical behavior for very small values of viscosity this difficulty can be overcome by using splitting methods derived for near integrable system this class of methods has positive real coefficients and can be used for non reversible systems such as burgers equation it also has the advantage of being able to account small viscosity in the accuracy the algorithm is based on the combination of implicit explicit finite difference schemes to solve each simplified problem and filtering technique to treat nonlinear instability the resulting algorithm is accurate efficient and easy to implement the new numerical results are compared with numerical and exact solutions reported in the literature and found that they are very accurate for small values of the viscosity

symmetries travelling wave and self similar solutions of the burgers hierarchy we examine the general element of the burgers hierarchy ut x xu nu 0 n 0 1 2 for its lie point symmetries we use these symmetries to construct traveling wave and self similar solutions we observe that the general member of the hierarchy can be rendered as a linear 1 1 evolution equation by means of an elementary riccati transformation and examine this equation for its lie point symmetries with the use of these symmetries we can construct the traveling wave and self similar solutions in closed form

a delay reaction diffusion model of the spread of bacteriophage infection this paper is a continuation of recent attempts to understand via mathematical modeling the dynamics of marine bacteriophage infections previous authors have proposed systems of ordinary differential delay equations with delay dependent coefficients in this paper we continue these studies in two respects first we show that the dynamics is sensitive to the phage mortality function and in particular to the parameter we use to measure the density dependent phage mortality rate second we incorporate spatial effects by deriving in one spatial dimension a delay reaction diffusion model in which the delay term is rigorously derived by solving a von foerster equation using this model we formally compute the speed at which the viral infection spreads through the domain and investigate how this speed depends on the system parameters numerical simulations suggest that the minimum speed according to linear theory is the asymptotic speed of propagation ks t p t di dt ii t ks t p t e it ks t t p t t dp dt pp t ks t p t be it ks t t p t t

a direct variational methods applied to burgers equation in this study a compact approximate method in limiting form for calculating the solution of burgers equation with appropriate boundary conditions is presented the results obtained by present method are found to be in good agreement with those due to earlier authors and offers appreciable advantages for burgers like nonlinear problems

a novel numerical scheme for solving burgers equation abstract in this paper we propose a novel numerical scheme for solving burgers equation the scheme is based on a cubic spline quasi interpolant and multi node higher order expansion which make the algorithm simple and easy to implement the numerical experiments show that the proposed method produces high accurate results

line based recognition using a multidimensional hausdorff distance a line feature based approach for model based recognition using a four dimensional hausdorff distance is proposed this approach reduces the problem of finding the rotation scaling and translation transformations between a model and an image to the problem of finding a single translation minimizing the hausdorff distance between two sets of points in a four dimensional space the implementation of the proposed algorithm can be naturally extended to higher dimensional spaces to efficiently find correspondences between n dimensional patterns the method performance and sensitivity to segmentation problems are quantitatively characterized using an experimental protocol with simulated data it is shown that the algorithm performs well is robust to occlusion and outliers and that it degrades nicely as the segmentation problems increase experiments with real images are also presented

pseudospectral differencing methods for characteristic roots of delay differential equations in d breda s maset and r vermiglio ima j numer anal 24 2004 pp 1 19 and d breda the infinitesimal generator approach for the computation of characteristic roots for delay differential equations using bdf methods research report udmi rr17 2002 dipartimento di matematica e informatica universita degli studi di udine udine italy 2002 the authors proposed to compute the characteristic roots of delay differential equations ddes with multiple discrete and distributed delays by approximating the derivative in the infinitesimal generator of the solution operator semigroup by runge kutta rk and linear multistep lms methods respectively in this work the same approach is proposed in a new version based on pseudospectral differencing techniques we prove the spectral accuracy convergence behavior typical of pseudospectral schemes as also illustrated by some numerical experiments

numerical solutions of nonlinear burgers equation with modified cubic b splines collocation method abstract in this paper a numerical method is proposed to approximate the solution of the nonlinear burgers equation the method is based on collocation of modified cubic b splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range we apply modified cubic b splines for spatial variable and derivatives which produce a system of first order ordinary differential equations we solve this system by using ssp rk43 or ssp rk54 scheme this method needs less storage space that causes less accumulation of numerical errors the numerical approximate solutions to the burgers equation have been computed without transforming the equation and without using the linearization illustrative eleven examples are included to demonstrate the validity and applicability of the technique easy and economical implementation is the strength of this method

higher order accurate numerical solution of unsteady burgers equation abstract higher order accurate finite difference schemes for solving the unsteady burgers equation which often arises in mathematical modeling used to solve problems in fluid dynamics are presented the unsteady burgers equation belongs to a few nonlinear partial differential equations which has an exact solution and it allows one to compare the numerical solution with the exact one and the properties of different numerical methods we propose an explicit finite difference scheme for a numerical solution of the heat equation with robin boundary conditions it has a sixth order approximation in the space variable and a third order approximation in the time variable as an application we developed numerical schemes for solving a numerical solution of burgers equation using the relationship between the heat and burgers equations this scheme has up to sixth order approximation in the space variables the main advantage of our approach is transition to one dimensional equation which essentially reduces the computation costs compared to other direct methods for solving the unsteady burgers equation the numerical results of test examples are found in good agreement with exact solutions for a wide range of reynolds number and confirm the approximation orders of the schemes proposed

a high order compact finite difference scheme and precise integration method based on modified hopf cole transformation for numerical simulation of n dimensional burgers system abstract this paper modifies a n dimensional hopf cole transformation to the n dimensional burgers system we obtain the n dimensional heat conduction equation through the modification of the hopf cole transformation then the fourth order precise integration method pim in combination with a spatially global sixth order compact finite difference cfd scheme is presented to solve the equation with high accuracy moreover coupling with the strang splitting method the scheme is extended to multi dimensional two three dimensional burgers system numerical results show that the proposed method appreciably improves the computational accuracy compared with the existing numerical method moreover the two dimensional and three dimensional examples demonstrate excellent adaptability and the numerical simulation results also have very high accuracy in medium reynolds numbers

numerical solution of nonlinear burgers equation using high accuracy multi quadric quasi interpolation in this paper a numerical method is presented to approximate the solution to nonlinear burgers equation which is related to many scientific research topics a numerical scheme by using high accuracy multi quadric quasi interpolation is presented in which a kind of multi quadric quasi interpolant is used to approximate the derivatives of the solution in spatial domain and finite difference is used to approximate the derivatives of the solution in temporal domain the advantage of the scheme is that it is mesh free and in each time step only a multi quadric quasi interpolant is employed so that the algorithm is easy to implement the numerical results of this scheme are also shown and compared with other numerical schemes

on the class of high order time stepping schemes based on pade approximations for the numerical solution of burgers equation abstract numerical solution of burgers equation is presented using finite difference methods in space and positivity preserving pade approximations in time a class of high order time stepping schemes is introduced for practical purposes first second third and fourth order schemes are constructed efficient parallel versions of these schemes are given using a splitting technique of rational functions accuracy of the schemes is demonstrated by solving a test problem and comparing numerical results with the exact solution time evolution graphs show the physical phenomenon of the problem convergence tables are given to verify the theoretical order of convergence

a mixed finite difference and boundary element approach to one dimensional burgers equation this paper presents a mixed method for the numerical solution of the one dimensional burgers equation this method uses mixed boundary elements in association with finite differences two standard problems are used to validated the algorithm comparisons are made with some of the existing numerical schemes and analytical solutions the proposed method performs well

numerical solutions of the burgers equation by the least squares quadratic b spline finite element method in this study a least squares quadratic b spline finite element method for calculating the numerical solutions of the one dimensional burgers like equations with appropriate boundary and initial conditions is presented three test problems have been studied to demonstrate the accuracy of the present method results obtained by the method have been compared with the exact solution of each problem and are found to be in good agreement with each other a fourier stability analysis of the method is also investigated

numerical solution of one dimesional burgers equation explicit and exact explicit finite difference methods this paper presents finite difference solution and analytical solution of the finite difference approximations based on the standard explicit method to the one dimensional burgers equation which arises frequently in the mathematical modelling used to solve problems in fluid dynamics results obtained by these ways for some modest values of viscosity have been compared with the exact fourier one it is shown that they are in good agreement with each other

a stage structured predator prey model of beddington deangelis type we formulate and study a robust stage structured predator prey model of beddington deangelis type functional response the time delay is the time taken from birth to maturity the beddington deangelis functional response is similar to the holling type 2 functional response but contains an extra term describing mutual interference by predators first we show that the predator coexists with prey permanently if and only if the predator s recruitment rate at the peak of prey abundance is larger than its death rate second we show that if the system is permanent then a sufficiently large degree of the predator interference can not only stabilize the system but also guarantee the stability of the system against the increase of the carrying capacity of prey and the increase of birth rate of the adult predator third we show both analytically and numerically that stability switches of interior equilibrium may occur as maturation time delay increases stability may change from stable to unstable to finally stable implying that a large delay can be stabilizing

stability switches and hopf bifurcations of an isolated population model with delay dependent parameters the dynamical behaviors of an isolated population model involving delay dependent parameters are investigated it is shown that the positive equilibrium switches from being stable to unstable and then back to stable as the delay increases and the hopf bifurcation occurs finite times between the two critical values of stability changes which can be analytically determined moreover the bifurcating periodic solutions are expressed analytically in an approximate form by the perturbation approach and floquet technique the direction and stability of the bifurcating periodic solutions are also determined finally the validity of the results is shown by the consistency with the numerical simulations

numerical solution of the nonlinear klein gordon equation a numerical method is developed to solve the nonlinear one dimensional klein gordon equation by using the cubic b spline collocation method on the uniform mesh points we solve the problem for both dirichlet and neumann boundary conditions the convergence and stability of the method are proved the method is applied on some test examples and the numerical results have been compared with the exact solutions the l 2 l and root mean square errors rms in the solutions show the efficiency of the method computationally

numerical solution of burgers equation with high order splitting methods in this work high order splitting methods have been used for calculating the numerical solutions of burgers equation in one space dimension with periodic dirichlet neumann and robin boundary conditions however splitting methods with real coefficients of order higher than two necessarily have negative coefficients and cannot be used for time irreversible systems such as burgers equations due to the time irreversibility of the laplacian operator therefore the splitting methods with complex coefficients and extrapolation methods with real and positive coefficients have been employed if we consider the system as the perturbation of an exactly solvable problem or one that can be easily approximated numerically it is possible to employ highly efficient methods to approximate burgers equation the numerical results show that both the methods with complex time steps having one set of coefficients real and positive say a i r and b i c and high order extrapolation methods derived from a lower order splitting method produce very accurate solutions of burgers equation

the new numerical method for solving the system of two dimensional burgers equations in this paper the system of two dimensional burgers equations are solved by local discontinuous galerkin ldg finite element method the new method is based on the two dimensional hopf cole transformations which transform the system of two dimensional burgers equations into a linear heat equation then the linear heat equation is solved by the ldg finite element method the numerical solution of the heat equation is used to derive the numerical solutions of burgers equations directly such a ldg method can also be used to find the numerical solution of the two dimensional burgers equation by rewriting burgers equation as a system of the two dimensional burgers equations three numerical examples are used to demonstrate the efficiency and accuracy of the method

on a finite difference scheme for burgers equation in this paper we study properties of numerical solutions of burger s equation burgers equation is reduced to the heat equation on which we apply the douglas finite difference scheme the method is shown to be unconditionally stable fourth order accurate in space and second order accurate in time two test problems are used to validate the algorithm numerical solutions for various values of viscosity are calculated and it is concluded that the proposed method performs well

stability and bifurcation in a delayed predator prey system with beddington deangelis functional response we consider a delayed predator prey system with beddington deangelis functional response the stability of the interior equilibrium will be studied by analyzing the associated characteristic transcendental equation by choosing the delay as a bifurcation parameter we show that hopf bifurcation can occur as the delay crosses some critical values the direction and stability of the hopf bifurcation are investigated by following the procedure of deriving normal form given by faria and magalhaes an example is given and numerical simulations are performed to illustrate the obtained results

numerical solution of the burgers equation by local discontinuous galerkin method abstract in this paper the burgers equation is transformed into the linear diffusion equation by using the hopf cole transformation the obtained linear diffusion equation is discretized in space by the local discontinuous galerkin method the temporal discretization is accomplished by the total variation diminishing runge kutta method numerical solutions are compared with the exact solution and the numerical solutions obtained by adomian s decomposition method finite difference method b spline finite element method and boundary element method the results show that the local discontinuous galerkin method is one of the most efficient methods for solving the burgers equation even with small viscosity coefficient it can get the satisfied solution

a numerical solution of burgers equation by modified adomian method in this paper the modified adomian s decomposition method for calculating a numerical solution of the one dimensional quasi linear the burgers equation is presented time discretization has been used in decomposition without using any transformation in the burgers equation such as hopf cole transformation the numerical results obtained by this way for various values of viscosity have been compared with the exact solution to show the efficiency of the method

stability and traveling fronts in lotka volterra competition models with stage structure this paper is concerned with a delay differential equation model for the interaction between two species the adult members of which are in competition the competitive effects are of the lotka volterra kind and in the absence of competition it is assumed that each species evolves according to the predictions of a simple age structured model which reduces to a single equation for the total adult population for each of the two species the model incorporates a time delay which represents the time from birth to maturity of that species thus the time delays appear in the adult recruitment terms the dynamics of the model are determined and global stability results are established for each equilibrium the equilibria of the model involve the maturation delays the criteria for global convergence to each equilibrium are sharp and involve these delays a reaction diffusion extension of the model is also studied for the case when only the adult members of each species can diffuse we prove the existence of a

a numerical solution of the burgers equation using cubic b splines in the present paper numerical solutions of the one dimensional burgers equation are obtained by a method based on collocation of cubic b splines over finite elements the accuracy of the proposed method is demonstrated by three test problems the numerical results are found in good agreement with exact solutions time space integration of the burgers equation yields a system of difference equation which is shown to be unconditionally stable

local rbf method for multi dimensional partial differential equations abstract in this paper a local meshless differential quadrature collocation method is utilized to solve multi dimensional reaction convection diffusion pdes numerically in some cases global version of the meshless method is considered as well the meshless methods approximate solution on scattered and uniform nodes in both local and global sense in the case of convection dominated pdes the local meshless method is coupled with an upwind technique to avoid spurious oscillations for this purpose a physically motivated local domain is utilized in the flow direction both regular and irregular geometries are taken into consideration numerical experiments are performed to demonstrate effective applications and accuracy of the meshless method on regular and irregular domains

an exponentially fitted method for solving burgers equation in this paper an exponentially fitted method is used to numerically solve the one dimensional burgers equation the performance of the method is tested on the model involving moderately large reynolds numbers the obtained numerical results show that the method is efficient stable and reliable for solving burgers equation accurately even involving high reynolds numbers for which the exact solution fails copyright 2009 john wiley sons ltd

a numerical method based on crank nicolson scheme for burgers equation abstract in this paper we present a solution based on crank nicolson finite difference method for one dimensional burgers equation burgers equation arises frequently in mathematical modeling of problems in fluid dynamics hopf cole transformation e hopf the partial differential equation u t uu x u xx commun pure appl math 3 1950 201 230 j d cole on a quasilinear parabolic equation occurring in aerodynamics quart appl math 9 1951 225 236 is used to linearize burgers equation the resulting heat equation is discretized by using crank nicolson finite difference scheme this method is shown to be unconditionally stable and second order accurate in space and time numerical results obtained by the present method have been compared with exact solution for different values of reynolds number

efficiently locating objects using the hausdorff distance the hausdorff distance is a measure defined between two point sets here representing a model and an image the hausdorff distance is reliable even when the image contains multiple objects noise spurious features and occlusions in the past it has been used to search images for instances of a model that has been translated or translated and scaled by finding transformations that bring a large number of model features close to image features and vice versa in this paper we apply it to the task of locating an affine transformation of a model in an image this corresponds to determining the pose of a planar object that has undergone weak perspective projection we develop a rasterised approach to the search and a number of techniques that allow us to locate quickly all transformations of the model that satisfy two quality criteria we can also efficiently locate only the best transformation we discuss an implementation of this approach and present some examples of its use

numerical solution of the burgers equation by automatic differentiation abstract we compute the solution of the one dimensional burgers equation by marching the solution in time using a taylor series expansion our approach does not require symbolic manipulation and does not involve the solution of a system of linear or non linear algebraic equations instead we use recursive formulas obtained from the differential equation to calculate exact values of the derivatives needed in the taylor series we illustrate the effectiveness of our method by solving four test problems with known exact solutions the numerical solutions we obtain are in excellent agreement with the exact solutions while being superior to other previously reported numerical solutions

a linearized numerical scheme for burgers like equations a linearized implicit finite difference method is presented to find numerical solutions of the one dimensional burgers like equations the method has been used successfully to obtain accurate numerical solutions even for small values of viscosity term n results obtained by the present method using a direct technique for some values of n have been compared with the exact values and are found to be in good agreement with each other

b spline galerkin methods for numerical solutions of the burgers equation the first order splitting method is applied to the burgers equation and two numerical algorithms are set up for this time splitted burgers equation using both quadratic and cubic b spline galerkin finite element techniques the unknowns in the equation is resolved with the b splines in space and standart crank nicolson differencing schemes is used to advance solution in time results of three numerical test problems are used to compare each schemes with available some results

analysis of a one dimensional free boundary flow problem a one dimensional free surface problem is considered it consists in burgers equation with an additional diffusion term on a moving interval the well posedness of the problem is investigated and existence and uniqueness results are obtained locally in time a semi discretization in space with a piecewise linear finite element method is considered a priori and a posteriori error estimates are given for the semi discretization in space a time splitting scheme allows to obtain numerical results in agreement with the theoretical investigations

an algorithm based on exponential modified cubic b spline differential quadrature method for nonlinear burgers equation in this paper the authors developed a new differential quadrature method exponential modified cubic b spline differential quadrature method expo mcb dqm by using exponential modified cubic b spline functions as test functions in the traditional differential quadrature method 32 the new method is tested on one and two dimensional nonlinear burgers equations to check the efficiency and accuracy of the proposed method five numerical problems have been considered the numerical results of the method are compared with some existing methods and found that the proposed numerical method produces more accurate results than existing methods stability analysis of the algorithm is also done by using matrix stability analysis method

a 2d 3d model based object tracking framework abstract this paper presents a robust framework for tracking complex objects in video sequences multiple hypothesis tracking mht algorithm reported in ieee trans pattern anal mach intell 18 2 1996 is modified to accommodate a high level representations 2d edge map 3d models of objects for tracking the framework exploits the advantages of mht algorithm which is capable of resolving data association uncertainty and integrates it with object matching techniques to provide a robust behavior while tracking complex objects to track objects in 2d a 4d feature is used to represent edge line segments and are tracked using mht in many practical applications 3d models provide more information about the object s pose i e rotation information in the transformation space which cannot be recovered using 2d edge information hence a 3d model based object tracking algorithm is also presented a probabilistic hausdorff image matching algorithm is incorporated into the framework in order to determine the geometric transformation that best maps the model features onto their corresponding ones in the image plane 3d model of the object is used to constrain the tracker to operate in a consistent manner experimental results on real and synthetic image sequences are presented to demonstrate the efficacy of the proposed framework

numerical solution of burgers equation by cubic hermite collocation method abstract in this paper numerical solution of the non linear burgers equation are obtained by using cubic hermite collocation method chcm the advantage of the method is continuity of the dependent variable and its derivative throughout the solution range a linear stability analysis shows that the numerical scheme based on crank nicolson approximation in time is unconditionally stable this method is applied on some test problems with different choice of collocation points to validate the accuracy of the method the obtained numerical results show that the method is efficient robust and reliable even for high reynolds numbers for which the exact solution fails moreover the method can be applied to a wide class of nonlinear partial differential equations

hybrid image matching combining hausdorff distance with normalized gradient matching image matching has been a central problem in computer vision and image processing for decades most of the previous approaches to image matching can be categorized into the intensity based and edge based comparison hausdorff distance has been widely used for comparing point sets or edge maps since it does not require point correspondences in this paper we propose a new image similarity measure combining the hausdorff distance with a normalized gradient consistency score for image matching the normalized gradient consistency score is designed to compare the normalized image gradient fields between two images to alleviate the illumination variation problem in image matching by combining the edge based and intensity based information for image matching we are able to achieve robust image matching under different lighting conditions we show the superior robustness property of the proposed image matching technique through experiments on face recognition under different lighting conditions

a sixth order compact finite difference scheme to the numerical solutions of burgers equation abstract a numerical solution of the one dimensional burgers equation is obtained using a sixth order compact finite difference method to achieve this a tridiagonal sixth order compact finite difference scheme in space and a low storage third order total variation diminishing runge kutta scheme in time have been combined the scheme is implemented to solve two test problems with known exact solutions comparisons of the computed results with exact solutions showed that the method is capable of achieving high accuracy and efficiency with minimal computational effort the present results are also seen to be more accurate than some available results given in the literature