iterative solution of a 3 d scattering problem from arbitrary shaped multidielectric and multiconducting bodies we present an iterative algorithm used for the computation of the scattering from arbitrary shaped bodies made of dielectric and conducting material the harmonic problem is discretized by a hybrid boundary integral method finite element method to solve the discretized linear system a modified version of a minimal residual algorithm has been developed for complex matrices it takes into account the lagrange multiplier constraint in a special way this modified version also allows the linear system to be solved for many right hand sides in an efficient manner

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

development of the kansa method for solving seepage problems using a new algorithm for the shape parameter optimization abstract in this research the kansa or multiquadric method mq has been developed for solving the seepage problems in 2d and 3d arbitrary domains this research is the first application of this method for seepage analysis in both confined and unconfined porous media the domain decomposition approach has been employed for applying mq method easily in inhomogeneous and irregular complex geometries and decreasing the computational costs for determining the optimum shape parameter that affects strongly the accuracy of mq and other rfb methods a new scheme that decreases drastically the computational time is introduced the efficiency of the proposed algorithm has been examined under various radial basis functions variations of number of interpolating points and points distribution through a numerical example with analytical solution eventually three examples including different boundary conditions are presented comparing results of the examples with other numerical methods indicates that the present approach has high capability and accuracy in solving seepage problems

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

hyperbolic conservation laws with relaxation the effect of relaxation is important in many physical situations it is present in the kinetic theory of gases elasticity with memory gas flow with thermo non equilibrium water waves etc the governing equations often take the form of hyperbolic conservation laws with lower order terms in this article we present and analyze a simple model of hyperbolic conservation laws with relaxation effects dynamic subcharacteristics governing the propagation of disturbances over strong wave forms are identified stability criteria for diffusion waves expansion waves and traveling waves are found and justified nonlinearly time asymptotic expansion and the energy method are used in the analysis for dissipative waves the expansion is similar in spirit to the chapman enskog expansion in the kinetic theory for shock waves however a different approach is needed

convergence of the fractional step lax friedrichs scheme and godunov scheme for the isentropic system of gas dynamics a convergence theorem of the fractional step lax friedrichs scheme and godunov scheme for an inhomogeneous system of isentropic gas dynamics 1 5 3 is established by using the framework of compensated compactness meanwhile a corresponding existence theorem of global solutions with large data containing the vacuum is obtained

nonlinear stability with decay rate for traveling wave solutions of a hyperbolic system with relaxation abstract we derive decay estimates for small disturbances of smooth traveling wave solutions of a one dimensional strictly hyperbolic system of partial differential equations with a zeroth order term which models relaxation in a number of physical systems

asymptotic behavior of solutions to a hyperbolic system with relaxation and boundary effect in this paper we study the initial boundary value problem of the following hyperbolic system with relaxation

l 1 convergence to the barenblatt solution for compressible euler equations with damping we study the asymptotic behavior of compressible isentropic flow through a porous medium when the initial mass is finite the model system is the compressible euler equation with frictional damping as t the density is conjectured to obey the well known porous medium equation and the momentum is expected to be formulated by darcy s law in this paper we prove that any l weak entropy solution to the cauchy problem of damped euler equations with finite initial mass converges strongly in the natural l1 topology with decay rates to the barenblatt profile of the porous medium equation the density function tends to the barenblatt solution of the porous medium equation while the momentum is described by darcy s law the results are achieved through a comprehensive entropy analysis capturing the dissipative character of the problem

convergence to equilibrium for the relaxation approximations of conservation laws we study the cauchy problem for 2 2 semilinear and quasilinear hyperbolic systems with a singular relaxation term special comparison and compactness properties are established by assuming the subcharacteristic condition therefore we can prove the convergence to equilibrium of the solutions of these problems as the singular perturbation parameter tends to 0 this research was strongly motivated by the recent numerical investigations of s jin and z xin on the relaxation schemes for conservation laws 1996 john wiley sons inc

convergence to traveling waves with decay rates for solutions of the initial boundary problem to a relaxation model abstract in this paper we consider a 2 2 relaxation hyperbolic system of conservation laws with a boundary effect and we show that the solutions of this initial boundary problem tend to the traveling wave solutions of the corresponding cauchy problem time asymptotically in particular we give the algebraic and exponential decay rates by using the weighted energy method the location of a shift for the traveling wave to overcome the difficulty in the boundary plays a key role in this paper

frequency localization duhamel principle and its application to the optimal decay of dissipative systems in low dimensions abstract recently a time decay framework l 2 r n b 2 s r n s 0 has been given by 49 for linearized dissipative hyperbolic systems which allows to pay less attention to the traditional spectral analysis however owing to interpolation techniques those decay results for nonlinear hyperbolic systems hold true only in higher dimensions n 3 and the analysis in low dimensions say n 1 2 was left open we try to give a satisfactory answer in the current work first of all we develop new time decay properties on the frequency localization duhamel principle and then it is shown that the classical solution and its derivatives of fractional order decay at the optimal algebraic rate in dimensions n 1 2 by using a new technique which is the so called piecewise duhamel principle in localized time weighted energy approaches compared to 49 finally as direct applications explicit decay statements are worked out for some relevant examples subjected to the same dissipative structure for instance damped compressible euler equations the thermoelasticity with second sound and timoshenko systems with equal wave speeds

nonlinear stability of shock fronts for a relaxation system in several space dimensions it is proposed by jin and xin in 3 to use the following relaxation system u t sum limits i 1 m left upsilon i right x i 0 text u in r n text upsilon i in r n 1 upsilon it a i u x i frac left upsilon i f i left u right right varepsilon text i 1 2 ldots m 2 to approximate multi dimensional hyperbolic conservation laws of the form u t sum limits i 1 m f i left u right x i 0 left x i t right in r 1 times r u in r n 3 here e is a positive constant representing the rate of relaxation and a i a i i a i 0 i 1 2 m with i being the n n identity matrix and a i being positive constants satisfying the subcharacteristic condition see 3 and sc one of the main advantages of the system 1 2 is its form of local relaxation structure and linearity in convection which makes it possible to solve this system quite easily by underresolved stable numerical discretizations using neither riemann solvers spatially nor nonlinear system of algebraic equations solvers temporally a class of numerical schemes solving 1 2 has been proposed in 3 which yields satisfactory numerical solutions to hyperbolic conservation laws 3 3 yet the asymptotic equivalence of the relaxation system 1 2 and the hyperbolic conservation laws 3 as either the rate of relaxation goes to zero or time approaches infinity has been rigorously analysed only in one space dimension see 5 9 and 11

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

l1 convergence rates to the barenblatt solution for the damped compressible euler equations abstract in our previous work 17 it is shown that any l weak entropy solution of damped compressible euler equation converges to the barrenblatt s solution with finite mass in l 1 norm with a convergence rate for 1 3 in this paper by introducing an elaborate iterative method and using the intensive entropy analysis we prove the l 1 convergence to the barrenblatt s solution for any large 3 furthermore we get better l 1 convergence rate for 2 3

quadratic b spline finite element method for numerical solution of the burgers equation abstract in this paper the one dimensional nonlinear burgers equation was converted to a set of nonlinear ordinary differential equations by the method of discretization in time and then each of them was solved by applying the quadratic b spline finite element method in order to show the efficiency of the presented method two problems were considered the numerical solutions obtained for various values of viscosity were compared with the exact solutions it is seen that the results obtained by this way are quite satisfactory

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

diffusive relaxation limit of classical solutions to the damped compressible euler equations abstract we construct uniform global classical solutions to the damped compressible euler equations on the framework of general besov spaces which includes both the usual sobolev spaces h s r d s 1 d 2 and the critical besov space b 2 1 1 d 2 r d such extension heavily depends on a revision of commutator estimates and an elementary fact that indicates the connection between homogeneous and inhomogeneous chemin lerner spaces furthermore we obtain the diffusive relaxation limit of euler equations towards the porous medium equation by means of aubin lions compactness argument

large time behavior of solutions for compressible euler equations with damping in r 3 we consider the long time behavior and optimal decay rates of global strong solutions for the isentropic compressible euler equations with damping in r3 in the present paper when the regular initial data belong to some sobolev space hl r3 b 1 s r3 with l 4 and s 0 1 we show that the density of the system converges to its equilibrium state at the rates 1 t 34 s2 in the l2 norm or 1 t 32 s2 in the l norm respectively the momentum of the system decays at the rates 1 t 54 s2 in the l2 norm or 1 t 2 s2 in the l norm respectively which are shown to be optimal for the compressible euler equations with damping

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

numerical solution of one dimensional sine gordon equation using high accuracy multiquadric quasi interpolation abstract in this paper we propose a numerical scheme to solve one dimensional sine gordon equation related to many scientific research topics by using high accuracy multiquadric quasi interpolation we use the derivatives of a multiquadric quasi interpolant to approximate the spatial derivatives and a finite difference to approximate the temporal derivative the advantages of the scheme are that it is meshfree and in each time step only a multiquadric quasi interpolant is employed so that the algorithm is very easy to implement the accuracy of our scheme is demonstrated by some test problems

existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in eulerian and lagrangian coordinates we prove the existence and compactness stability of entropy solutions for the hyperbolic systems of conservation laws corresponding to the isentropic gas dynamics where the pressure and density are related by a law for any 1 our results considerably extend and simplify the program initiated by diperna and provide a complete existence proof our methods are based on the compensated compactness and the kinetic formulation of systems of conservation laws 1996 john wiley sons inc

numerical schemes for hyperbolic systems of conservation laws with stiff diffusive relaxation hyperbolic systems of conservation laws often have diffusive relaxation terms that lead to a small relaxation limit governed by reduced systems of a parabolic or hyperbolic type in such systems the understanding of basic wave pattern is difficult to achieve and standard high resolution methods fail to describe the right asymptotic behavior unless the small relaxation rate is numerically resolved we develop high resolution underresolved numerical schemes that possess the discrete analogue of the continuous asymptotic limit which are thus able to approximate the equilibrium system with high order accuracy even if the limiting equations may change type

asymptotics in nonlinear evolution system with dissipation and ellipticity on quadrant abstract in this paper we consider an initial boundary value problem for some nonlinear evolution system with dissipation and ellipticity we establish the global existence and furthermore obtain the l p p 2 decay rates of solutions corresponding to diffusion waves the analysis is based on the energy method and pointwise estimates

a univariate quasi multiquadric interpolationwith better smoothness in this paper we propose a multilevel univariate quasi interpolation scheme usingmultiquadric basis it is practical as it does not require derivative values of the function being interpolated it has a higher degree of smoothness than the original level 0 formula as it allows a shape parameter c o h our level 1 quasi interpolation costs o email protected n flops to set up it preserves strict convexity and monotonicity when c o h we prove the proposed scheme converges with a rate of o h 2 email protected h furthermore if both a and are relatively small compared with email protected the convergence rate will increase we verify numerically that c h is a good shape parameter to use for our method hence we need not find the optimal parameter for all test functions both convergence speed and error are optimized for c between 0 5h and 1 5h our method can be generalized to a multilevel scheme we include the numerical results for the level 2 scheme the shape parameter of the level 2 scheme can be chosen between 2h to 3h

pointwise estimates and lp convergence rates to diffusion waves for p system with damping abstract by introducing a new approximate green function we obtain the pointwise estimates on the solutions of euler equations with linear frictional damping from which we can deduce the optimal l p 1 p convergence rates to the nonlinear diffusion waves the pointwise estimates and l p 1 p convergence rates given in this paper are new

the biconjugate gradient method for electromagnetic scattering the biconjugate gradient bcg method for solving linear systems is shown to be more efficient than the conjugate gradient cg method for several examples from electromagnetic scattering a remedy for the occasional stagnation of the algorithm is proposed the potential flaw in the bcg algorithm may be avoided when encountered by restarting the algorithm with a perturbed estimate of the solution

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

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

hyperbolic to parabolic relaxation theory for quasilinear first order systems abstract in this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type in particular we obtain a complete theory for the 2 2 systems of genuinely nonlinear hyperbolic balance laws in 1 d with a strong dissipative term a different method which combines the div curl lemma with accretive operators is then applied to study the limiting profiles in the case of nonhomogeneous isentropic gas dynamics we also investigate relaxation results for some 2 d cases which include the cattaneo model for nonlinear heat conduction and the compressible euler flow moreover convergence result is also obtained for general semilinear systems in 1 d

propagation of a stationary shock layer in the presence of a boundary we are interested in the large time behavior of a stationary shock layer in the presence of a boundary effect it is shown that the stationary shock propagates away from the boundary with speed inversely proportional to the time t consequently the location of the wave front is of order log thinspace 1 t we show therefore that the zero viscosity and time asymptotic limits do not commute our analysis involves detailed point wise estimates which allow us to trace the shock

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

decay rates of solutions to the cauchy problem for dissipative nonlinear evolution equations abstract in this paper we study the global existence and the asymptotic behavior of the solutions to the cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects e t 1 x x x t 1 x x x x with initial data i x 0 0 x 0 x as x where and are positive constants such that 1 1 through constructing a correct function x t defined by 2 13 and using the energy method we show sup x r x t x x x t 0 as t and the solutions decay with exponential rates the same problem was studied by tang and zhao s q tang h j zhao nonlinear stability for dissipative nonlinear evolution equations with ellipticity j math anal appl 233 1999 336 358 for the case of 0 0

uniform global existence and parabolic limit for partially dissipative hyperbolic systems abstract this work concerns smooth solutions to the cauchy problem for first order partially dissipative hyperbolic systems with a small parameter the systems are written in non conservative form in several space variables we introduce algebraic conditions on the structure of the systems under these conditions together with a partial dissipation condition and the shizuta kawashima stability condition we prove three main results around constant equilibrium states these results are uniform global existence with respect to the parameter global in time convergence of the systems to second order nonlinear parabolic systems in a slow time variable and global existence when the parameter is fixed we also give examples of physical models to which the above results can be applied

nonlinear stability of strong rarefaction waves for the generalized kdv burgers kuramoto equation with large initial perturbation abstract in was shown in ruan et al 2008 3 that rarefaction waves for the generalized kdv burgers kuramoto equation are nonlinearly stable provided that both the strength of the rarefaction waves and the initial perturbation are sufficiently small the main purpose of this work is concerned with nonlinear stability of strong rarefaction waves for the generalized kdv burgers kuramoto equation with large initial perturbation in our results we do not require the strength of the rarefaction waves to be small and when the smooth nonlinear flux function satisfies certain growth condition at infinity the initial perturbation can be chosen arbitrarily in h 1 r while for a general smooth nonlinear flux function we need to ask for the l 2 norm of the initial perturbation to be small but the l 2 norm of the first derivative of the initial perturbation can be large and consequently the h 1 r norm of the initial perturbation can also be large

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

weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift diffusion equation we investigate the relaxation problem for the hydrodynamic isentropic euler poisson system when the momentum relaxation time tends to zero very sharp estimates on the solutions independent of the relaxation time are obtained and used to establish compactness

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

convergence to the barenblatt solution for the compressible euler equations with damping and vacuum we study the asymptotic behavior of a compressible isentropic flow through a porous medium when the initial mass is finite the model system is the compressible euler equation with frictional damping as t the density is conjectured to obey the well known porous medium equation and the momentum is expected to be formulated by darcy s law in this paper we give a definite answer to this conjecture without any assumption on smallness or regularity for the initial data we prove that any l weak entropy solution to the cauchy problem of damped euler equations with finite initial mass converges strongly in lp with decay rates to matching barenblatt s profile of the porous medium equation the density function tends to the barenblatt s solution of the porous medium equation while the momentum is described by darcy s law

asymptotic stability of traveling wave solutions of systems for one dimensional gas motion the asymptotic stability of traveling wave solutions with shock profile is investigated for several systems in gas dynamics 1 the solution of a scalar conservation law with viscosity approaches the traveling wave solution at the ratet for some 0 ast provided that the initial disturbance is small and of integral zero and in addition decays at an algebraic rate for x 2 the traveling wave solution with nishida and smoller s condition of the system of a viscous heat conductive ideal gas is asymptotically stable provided the initial disturbance is small and of integral zero 3 the traveling wave solution with weak shock profile of the broadwell model system of the boltzmann equation is asymptotically stable provided the initial disturbance is small and its hydrodynamical moments are of integral zero each proof is given by applying an elementary energy method to the integrated system of the conservation form of the original one the property of integral zero of the initial disturbance plays a crucial role in this procedure

global existence and large time behavior for the system of compressible adiabatic flow through porous media in r 3 abstract the system of compressible adiabatic flow through porous media is considered in r 3 in the present paper the global existence and uniqueness of classical solutions are obtained when the initial data is near its equilibrium we also show that the pressure of the system converges to its equilibrium state at the same l 2 rate 1 t 3 4 as the navier stokes equations without heat conductivity but the velocity of the system decays at the l 2 rate 1 t 5 4 which is faster than the l 2 rate 1 t 3 4 for the navier stokes equations without heat conductivity duan and ma 2008 3

cauchy problem for an isentropic magnetogasdynamic system abstract this paper investigates the cauchy problem for an isentropic magnetogasdynamic system under certain reasonable hypotheses on the initial data we obtain the global existence and uniqueness of the c 1 solution to the system meanwhile when the hypotheses on the initial data do not hold we obtain the blow up phenomena of the c 1 solution to the system the bounds of the solution are shown to depend on the parameter which characterizes a one dimensional plane flow 0 or a three dimensional cylindrically symmetric flow 1 it is shown that the existence of the finite time singularity is significantly influenced by the magnetic field strength present in the flow along with the initial data

a chebyshev spectral collocation method for solving burgers type equations in this paper we elaborated a spectral collocation method based on differentiated chebyshev polynomials to obtain numerical solutions for some different kinds of nonlinear partial differential equations the problem is reduced to a system of ordinary differential equations that are solved by runge kutta method of order four numerical results for the nonlinear evolution equations such as 1d burgers kdv burgers coupled burgers 2d burgers and system of 2d burgers equations are obtained the numerical results are found to be in good agreement with the exact solutions numerical computations for a wide range of values of reynolds number show that the present method offers better accuracy in comparison with other previous methods moreover the method can be applied to a wide class of nonlinear partial differential equations

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

long time existence and singular perturbation results for quasilinear hyperbolic equations with small parameter and dissipation term iii on considere des solutions lisses du probleme aux valeurs initiales hyperbolique quasilineaire eu tt u t ij 1 n a ij i j u 0 u 0 u 0 u t 0 u 1 ou e 0 0 u u x t r x r n on etudie l existence de solutions globales correspondant a des donnees arbitrairement grandes initiales u 0 et u 1 et a leur convergence quand e 0 vers la solution du probleme parabolique correspondant

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

high order multi symplectic schemes for the nonlinear klein gordon equation in this paper we construct multi symplectic schemes with any order of accuracy for the nonlinear klein gordon equation by concatenating the symplectic schemes for odes some existing schemes such as the preissman scheme and the leap frog scheme and new multi symplectic schemes are constructed we also show that the composition method which plays a crucial role in finding the high order symplectic integrators for the odes can also be applied to construct high order multi symplectic schemes for pdes extension of the concatenating method to more than one space dimension is also discussed numerical experiments are presented to show the order and the efficiency of the constructed multi symplectic schemes

asymptotic stability of rarefaction waves for the generalized kdv burgers equation on the half line abstract we investigate the asymptotic behavior of solutions of the initial boundary value problem for the generalized kdv burgers equation u t f u x u x x u x x x on the half line with the boundary condition u 0 t u the corresponding cauchy problems of the behaviors of weak and strong rarefaction waves have respectively been studied by wang and zhu z a wang c j zhu stability of the rarefaction wave for the generalized kdv burgers equation acta math sci 22b 3 2002 309 328 and duan and zhao r duan h j zhao global stability of strong rarefaction waves for the generalized kdv burgers equation nonlinear anal tma 66 2007 1100 1117 in the present problem on the basis of the dirichlet boundary conditions the asymptotic states are divided into five cases dependent on the signs of the characteristic speeds f u in the cases of 0 f u f u we prove the global existence of solutions and asymptotic stability of the weak rarefaction waves when the initial disturbance is small also we can get asymptotic stability of the strong rarefaction waves when f u satisfies a certain growth condition

convergence of the conjugate gradient method when applied to matrix equations representing electromagnetic scattering problems an iterative procedure based on the conjugate gradient method is used to solve a variety of matrix equations representing electromagnetic scattering problems in an attempt to characterize the typical rate of convergence of that method it is found that this rate depends on the cell density per wavelength used in the discretization the presence of symmetries in the solution and the degree to which mixed cell sizes are used in the models assuming cell densities used in the discretization are in the range of ten per linear wavelength the iterative algorithm typically requires n 4 to n 2 steps to converge to necessary accuracy where n is the order of the matrix under consideration

a galerkin finite element approach to burgers equation a galerkin finite element method is presented for the numerical solution of burgers equation a linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is found via a crank nicolson approach involving a product approximation it is shown that this method is capable of solving burgers equation accurately for a wide range of viscosity values the results show that the new method performs better than the most of the methods available in the literature

kinetic formulation of the isentropic gas dynamics and p systems we consider the 2 x 2 hyperbolic system of isentropic gas dynamics in both eulerian or lagrangian variables also called the p system we show that they can be reformulated as a kinetic equation using an additional kinetic variable such a formulation was first obtained by the authors in the case of multidimensio nal scalar conservation laws a new phenomenon occurs here namely that the advection velocity is now a combination of the macroscopic and kinetic velocities various applications are given we recover the invariant regions deduce new l estimates using moments lemma and prove l w stability for 7 3

global stability of strong rarefaction waves for the generalized kdv burgers equation this paper is concerned with the global stability of strong rarefaction waves for the generalized kdv burgers equation in contrast to former results obtained by z a wang and c j zhu stability of the rarefaction wave for the generalized kdv burgers equation acta math sci 22b 3 2002 319 328 ours do not require the strength of the rarefaction waves to be small and the initial disturbance can also be chosen large c 2006 elsevier ltd all rights reserved

a class of high order compact difference schemes for solving the burgers equations abstract in this paper a class of high order compact difference method is introduced for solving the burgers equations firstly a linear high order compact difference scheme is proposed to solve the one dimensional burgers equation the scheme is fourth order accurate in space and second order accurate in time linear stability analysis is conducted to show the scheme is conditionally stable because only three grid points are involved in each time level thomas algorithm can be directly used to solve the tridiagonal linear system then this method is extended to solve the two dimensional and three dimensional coupled burgers equations numerical experiments are carried out to demonstrate the accuracy and dependability of the present method

zero relaxation limit to centered rarefaction waves for jin xin relaxation system abstract in this paper we study the zero relaxation limit problem for the following jin xin relaxation system e u t v x 0 v t a 2 u x 1 f u v with initial data i u v x 0 u 0 x v 0 x u v u 0 as x this system was proposed by jin and xin 1995 1 with an interesting numerical origin as the relaxation time tends to zero this system converges to the equilibrium conservation law formally our interest is to study the case where the initial data are allowed to have jump discontinuities such that the corresponding solutions to the equilibrium conservation law contain centered rarefaction waves and the limits u v of the initial data at x do not satisfy the equilibrium equation i e v f u in particular riemann data connected by rarefaction curves are included we show that if the wave strength is sufficiently small then the solution for the relaxation system exists globally in time and converges to the solution of the corresponding rarefaction waves uniformly as the relaxation time goes to zero except for an initial layer

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

lanczos type variants of the cocr method for complex nonsymmetric linear systems motivated by the celebrated extending applications of the well established complex biconjugate gradient cbicg method to deal with large three dimensional electromagnetic scattering problems by pocock and walker m d pocock s p walker the complex bi conjugate gradient solver applied to large electromagnetic scattering problems computational costs and cost scalings ieee trans antennas propagat 45 1997 140 146 three lanczos type variants of the recent conjugate a orthogonal conjugate residual cocr method of sogabe and zhang t sogabe s l zhang a cocr method for solving complex symmetric linear systems j comput appl math 199 2007 297 303 are explored for the solution of complex nonsymmetric linear systems the first two can be respectively considered as mathematically equivalent but numerically improved popularizing versions of the bicr and crs methods for complex systems presented in sogabe s ph d dissertation and the last one is somewhat new and is a stabilized and more smoothly converging variant of the first two in some circumstances the presented algorithms are with the hope of obtaining smoother and hopefully faster convergence behavior in comparison with the cbicg method as well as its two corresponding variants this motivation is demonstrated by numerical experiments performed on some selective matrices borrowed from the university of florida sparse matrix collection by davis

global stability of the rarefaction wave of a one dimensional model system for compressible viscous gas this paper is concerned with the asymptotic behavior toward the rarefaction wave of the solution of a one dimensional barotropic model system for compressible viscous gas we assume that the initial data tend to constant states atx respectively and the riemann problem for the corresponding hyperbolic system admits a weak continuous rarefaction wave if the adiabatic constant satisfies 1 2 then the solution is proved to tend to the rarefaction wave ast under no smallness conditions of both the difference of asymptotic values atx and the initial data the proof is given by an elementaryl 2 energy method

a transpose free quasi minimal residual variant of the cors method for solving non hermitian linear systems recently the conjugate a orthogonal residual squared cors method is often competitive and superior to other krylov subspace methods for solving complex non hermitian linear systems from many realistic problems however like the conjugate gradient squared cgs method the cors method often exhibits irregular convergence behavior with wild oscillations in the residual norm to try and remedy this problem we develop a transpose free quasi minimal residual tfqmr variant of the cors method which leads to smooth convergence curves with a convergence rate similar to the cors method we also give convergence results for this new method finally numerical examples are reported to illustrate the effectiveness of the proposed method

a case study of global stability of strong rarefaction waves for 2 2 hyperbolic conservation laws with artificial viscosity this paper is concerned with the global stability of strong rarefaction waves for a class of 2 x 2 hyperbolic conservation laws with artificial viscosity i e the p system with artificial viscosity

convergence of singular limits for multi d semilinear hyperbolic systems to parabolic systems in this paper we investigate the diffusive zero relaxation limit of the following multi d semilinear hyperbolic system in pseudodifferential form w t x t 1 ea x d w x t 1 e 2 b x w x t 1 e d w x t e w x t we analyze the singular convergence as e 0 in the case which leads to a limit system of parabolic type the analysis is carried out by using the following steps i we single out algebraic structure conditions on the full system motivated by formal asymptotics by some examples of discrete velocity models in kinetic theories ii we deduce energy estimates uniformly in e by assuming the existence of a symmetrizer having the so called block structure and by assuming dissipativity conditions on b iii we assume a kawashima type condition and perform the convergence analysis by using generalizations of compensated compactness due to tartar and gerard finally we include examples that show how to use our theory to approximate any quasilinear parabolic systems satisfying the petrowski parabolicity condition or general reaction diffusion systems including chemotaxis and brusselator type systems

the complex bi conjugate gradient solver applied to large electromagnetic scattering problems computational costs and cost scalings the complex bi conjugate gradient iterative method is applied to an isoparametric boundary integral equation formulation for frequency domain electromagnetic scattering problems it is demonstrated to work well on large and geometrically complex examples including a 20 wavelength slender dipole the nasa almond and a resonant cavity on such problems with asymmetric curvilinear irregular meshes and nontrivial geometries the number of iterations required seems to increase rather more than linearly with body size indicating an overall spl sim sixth power cost scaling this scaling is essentially as for direct methods but with costs still a small fraction of the direct approach a method is proposed for the selection of a termination condition designed to avoid seeking the approximate answer too precisely it typically permits a further halving of costs