a block triple relaxation time lattice boltzmann model for nonlinear anisotropic convection diffusion equations abstract a block triple relaxation time b trirt lattice boltzmann model for general nonlinear anisotropic convection diffusion equations nacdes is proposed and the chapman enskog analysis shows that the present b trirt model can recover the nacdes correctly there are some striking features of the present b trirt model firstly the relaxation matrix of b trirt model is partitioned into three relaxation parameter blocks rather than a diagonal matrix in general multiple relaxation time mrt model secondly based on the analysis of half way bounce back hbb scheme for dirichlet boundary conditions we obtain an expression to determine the relaxation parameters thirdly the anisotropic diffusion tensor can be recovered by the relaxation parameter block that corresponds to the first order moment of non equilibrium distribution function a number of simulations of isotropic and anisotropic convection diffusion equations are conducted to validate the present b trirt model the results indicate that the present model has a second order accuracy in space and is also more accurate and more stable than some available lattice boltzmann models

comparisons of lattice boltzmann and finite difference methods for a two dimensional viscous burgers equation lattice boltzmann methods have been proposed as a computational means for solving various partial differential equations we look at three lattice boltzmann methods and an analogous finite difference method for solving a two dimensional scalar viscous burgers equation with periodic boundary conditions first using monotonicity arguments we prove that in the ell 1 norm the lattice boltzmann methods converge first order temporally and second order spatially then we provide some computational results which substantiate the theoretical results finally we compare the lattice boltzmann and finite difference methods the basis of comparison includes numerical results with regard to accuracy order of convergence performance and timing measurements memory requirements and conservations laws

on continuous solutions of a class of systems of nonlinear functional difference equations with deviating argument abstract bounded continuous solutions on r of a class of systems of nonlinear functional difference equations with a complicated nonlinear deviation of the argument that depends on unknown functions are studied here

on a solvable system of difference equations of kth order it is shown that the next system of k difference equationsx n j a n j x n k j b n j i 1 kx n i s j i 1 c n j n n 0 j 1 k where a n j b n j c n j

the modified extended tanh function method for solving burgers type equations abstract by means of the modified extended tanh function metf method the multiple travelling wave solutions of some different kinds of nonlinear partial differential equations are presented and implemented in a computer algebraic system solutions for the nonlinear equations such as one dimensional burgers kdv burgers coupled burgers and two dimensional burgers equations are obtained precisely and so the efficiency of the method can be demonstrated

on families of bounded continuous solutions of some systems of functional difference equations on half intervals some sufficient conditions for the existence of families of bounded continuous solutions of some classes of systems of functional difference equations on the intervals 0 and 0 are given

solutions of a system of functional differential equations in a right neighborhood of zero abstract we give some sufficient conditions for the system of nonlinear functional differential equations x qt x t f t x t x 1 qt x 2 qt x k qt x qt x g t where q 0 1 and functions f 0 t r n r n r n r n j 0 t r n 0 t j 1 k and g 0 t 0 t are continuous for the unique existence of continuously differentiable solutions x t on the interval 0 t 0 t satisfying the condition x 0 0

a modified multiple relaxation time lattice boltzmann model for convection diffusion equation a modified lattice boltzmann model with multiple relaxation times mrt for the convection diffusion equation cde is proposed by modifying the relaxation matrix as well as choosing the corresponding equilibrium distribution function properly the present model can recover the cde with anisotropic diffusion coefficient with no deviation term even when the velocity vector varies generally with space or time through the chapman enskog analysis this model is firstly validated by simulating the diffusion of a gaussian hill which demonstrates it can handle the anisotropic diffusion problem correctly then it is adopted to calculate the longitudinal dispersion coefficient of the taylor aris dispersion numerical results show that the present model can further reduce the numerical error under the condition of non zero velocity vector especially when the dimensionless relaxation time is relatively large

on a system of two nonlinear difference equations abstract in this paper we study the oscillatory behavior the boundedness of the solutions and the global asymptotic stability of the positive equilibrium of the system of two nonlinear difference equationsxn 1 a yn xn p yn 1 a xn yn q n 0 1 p qare positive integers

global attractivity of a family of nonautonomous max type difference equations abstract this paper studies a family of nonautonomous max type difference equations with several delays using some transformations we prove global attractivity of positive solutions to these equations under some conditions some of our results considerably extend related ones in the literature two examples are given to illustrate the main results

on some solvable systems of difference equations abstract we show that the following systems of difference equations x n 1 u n 1 v n y n 1 w n 1 s n n n 0 where u n v n w n s n are some of the sequences x n or y n with real initial values x 0 and y 0 are solvable in fourteen out of sixteen possible cases two cases are left unsolved probably the most interesting is the result in the case u n x n v n x n w n x n s n y n where a fascinating formula is obtained in an elegant way by using some ad hoc ideas

a lattice boltzmann scheme for incompressible multiphase flow and its application in simulation of rayleigh taylor instability in this paper we propose a new lattice boltzmann scheme for simulation of multiphase flow in the nearly incompressible limit the new scheme simulates fluid flows based on distribution functions the interfacial dynamics such as phase segregation and surface tension are modeled by incorporating molecular interactions the lattice boltzmann equations are derived from the continuous boltzmann equation with appropriate approximations suitable for incompressible flow the numerical stability is improved by reducing the effect of numerical errors in calculation of molecular interactions an index function is used to track interfaces between different phases simulations of the two dimensional rayleigh taylor instability yield satisfactory results the interface thickness is maintained at 3 4 grid spacings throughout simulations without artificial reconstruction steps

on some linear difference equations and inequalities with continuous argument abstract we study some properties of solutions of linear difference equations and inequalities with continuous argument in terms of the location of the zeroes of the characteristic polynomial of the associated homogeneous linear difference equation with constant coefficients

on a nonlinear second order system of difference equations we prove that all positive solutions of the next system of difference equationsx n 1 a y n px n 1 q y n 1 a x n py n 1 q email protected n 0 where parameters a p and q are positive numbers are bounded if one of the following conditions is satisfied p 2 4 or p 1 q q 1 completely describing the boundedness character of the system in this case

domains of undefinable solutions of some equations and systems of difference equations for some classes of difference equations and systems of difference equations we find the sets of initial values for which solutions of these equations and systems are not well defined so called domains of undefinable solutions

bounded solutions of some systems of nonlinear functional differential equations with iterated deviating argument abstract for a class of systems of nonlinear functional differential equations with iterated deviating arguments dependent of unknown functions are given some conditions for the existence of bounded solutions on the real line satisfying some additional conditions

asymptotically convergent solutions of a system of nonlinear functional differential equations of neutral type with iterated deviating arguments some conditions that guarantee the existence of a family of solutions converging to zero of a system of nonlinear functional differential equations with iterated deviating arguments are given

unique existence of bounded continuous solutions on the real line of a class of nonlinear functional equations with complicated deviations abstract the existence and uniqueness of bounded continuous solutions on the real line of a general class of nonlinear functional equations with quite complicated deviations dependent of unknown functions are established in this paper

more on a rational second order difference equation abstract here we give natural explanations for some recent relations for the solutions of the following difference equation z n 2 z n 1 3 z n 2 2 z n 1 2 n n 0 and extend them for the case of complex initial values we also present some other properties related to solutions of the equation as well as some properties of the solutions of an associate difference equation of first order

on fourteen solvable systems of difference equations abstract in this paper we mainly consider the systems of difference equations x n 1 1 p n q n y n 1 1 r n s n n n 0 where each of the sequences p n q n r n and s n represents either the sequence x n or the sequence y n with nonzero real initial values x 0 and y 0 then we solve fourteen out of sixteen possible systems it is noteworthy to depict that the solutions are presented in terms of fibonacci numbers for twelve systems of these fourteen systems

global stability of some symmetric difference equations suppose r 0 1 m n and 1 k1 k2 k2m 1 and let s2m 1 1 2 2m 1 we show that every positive solution to the difference equation yn p2m 12m 1 yn k1r yn k2r yn k2m 1r p2m2m 1 yn k1r yn k2r yn k2m 1r n n0 where p2m 12m 1 x1 x2 x2m 1 r 1rodd2m 1 t1 t2 tr s2m 1t1 t2 trxt1xt2 xtr and p2m2m 1 x1 x2 x2m 1 1 r 2reven2m t1 t2 tr s2m 1t1 t2 trxt1xt2 xtr converges to one this result confirms a quite recent conjecture posed by liu and yang 2010 in 10 we also prove another result regarding a related equation

on some systems of difference equations abstract in this note we show that the following systems of difference equations u n 1 v n 1 v n v n 1 u n 1 u n u n 1 v n 1 u n v n 1 u n 1 v n u n 1 u n 1 v n v n 1 v n 1 u n with n n 0 and complex initial values u 0 and v 0 are solvable explicitly by means of riccati equations and based on the formulae for the general solutions we present the behaviour of their solutions as n while the result is natural for the first system it is a bit surprising for the other two systems

on a system of difference equations of odd order solvable in closed form it is shown that the next system of difference equationsx n c ny n 2 k 1 a n b ny n 2 k 1 i 1 k 1y n 2 i 1 x n 2 i y email protected nx n 2 k 1 a email protected nx n 2 k 1 i 1 k 1x n 2 i 1 y n 2 email protected n 0 where a n b n c n a n b n c n email protected n 0 and initial values x i y i email protected 1 2 2k 1 are real numbers is solved in closed form and the behavior of its well defined solutions when all the coefficients in the system are constant is described

on the difference equation xn xn 2 bn cnxn 1xn 2 abstract we prove that the difference equation x n x n 2 b n c n x n 1 x n 2 n n 0 where b n n n 0 and c n n n 0 are sequences periodic with period two and the initial values x 2 x 1 are real numbers can be solved explicitly some applications of obtained formulae are given

global stability of a difference equation with maximum we prove that every positive solution to the difference equationx n maxa 1x n 1 a 1 a 2x n 2 a 2 a kx n k a k email protected n 0 where email protected n a i 0 a email protected 0 1 i 1 k converges to the following quantity maxa 1 1 a 1 1 a k 1 a k 1 confirming a quite recent conjecture of interest we also prove another result on global convergence which concerns some cases when not all a i i 1 k belong to the interval 0 1

on the system of two difference equations xn 1 i 0kai yn ipi yn 1 i 0kbi xn iqi abstract in this paper we study the system of two difference equations of the form x n 1 i 0 k a i y n i p i y n 1 i 0 k b i x n i q i where a i b i i 0 1 k x i y i i k k 1 0 are positive numbers and p i q i i 0 k are positive constants more precisely we investigate the boundedness the persistence of the positive solutions the existence of a unique positive equilibrium and the global asymptotic stability of the positive equilibrium of the above system finally we find solutions of the system which do not oscillate about the positive equilibrium

asymptotic convergence of the solutions of a discrete system with delays abstract a system of s discrete equations y n n y n j y n k is considered where k and j are integers k j 0 n is a real s s square matrix defined for n n 0 k n 0 z with non negative elements ij n i j 1 s such that j 1 s ij n 0 y y 1 y 2 y s t n 0 k n 0 k 1 r s and y n y n 1 y n for n n 0 a method of auxiliary inequalities is used to prove that every solution of the given system is asymptotically convergent under some conditions i e for every solution y n defined for all sufficiently large n there exists a finite limit lim n y n moreover it is proved that the asymptotic convergence of all solutions is equivalent to the existence of one asymptotically convergent solution with increasing coordinates some discussion related to the so called critical case known for scalar equations is given as well

global stability and asymptotics of some classes of rational difference equations in this note we prove that the positive solutions of some classes of rational difference equations are globally asymptotically stable using a berg s result we also find asymptotics of some solutions of these equations

on solutions of a class of systems of nonlinear functional differential equations of neutral type with complicated deviations of an argument abstract sufficient conditions for the existence of a unique bounded solution together with its first derivative on r of a system of nonlinear functional differential equations with an iterated deviating argument dependent of unknown function and satisfying the condition lim t x t 1 x t 0 are given

eventual periodicity of some systems of max type difference equations the periodicity of the next system of max type difference equations xn 1 max1 i1 m1f1i1xn ki1 1 1 1 xn ki1 2 1 2 xn ki1 l 1 l n xn t1s 1 xn 2 max1 i2 m2f2i2xn ki2 1 2 1 xn ki2 2 2 2 xn ki2 l 2 l n xn t2s 2 xn l max1 il mlflilxn kil 1 l 1 xn kil 2 l 2 xn kil l l l n xn tls l n n0n n0 where s l mj tj kij h j n j h 1 l j h 1 l 1 2 l 1 2 l is a permutation of 1 2 l 1 2 l and fjij 0 l n0 0 fjij 0 l n0 0 j 1 l j 1 l ij 1 mj ij 1 mj is studied it is shown that under some conditions posed on functions fjijfjij all positive solutions of the system are eventually periodic with period ts for some t nt n

asymptotic behavior of the positive solutions of an exponential type system of difference equations in this paper we study the existence of a unique positive equilibrium the boundedness persistence and global attractivity of the positive solutions of a system of the following two difference equations x n 1 ax n by n 1 e x n y n 1 cy n dx n 1 e y n n 0 1 where a b c d are positive constants and the initial values x 1 x 0 y 1 y 0 are positive numbers

on a solvable system of difference equations of fourth order it is shown that the next system of k difference equationsx n j a n j x n k j b n j i 1 kx n i s j i 1 c n j n n 0 j 1 k where a n j b n j c n j n n 0 j 1 k and initial values x i j i j 1 k are real numbers and where s n 1 k is defined by s km j j 1 j 1 k 1 s km k 1 m n 0 can be solved in closed form in an elegant way some applications of obtained formulas for the case when the sequences a n j b n j and c n j are k periodic are also given

on the difference equation xn xn kb cxn 1 xn k abstract we describe the behavior of well defined solutions of the difference equation x n x n k b cx n 1 x n k n n 0 where k n parameters b c and the initial values x k x 1 are real numbers these results among others improve and extend our results in s stevic more on a rational recurrence relation appl math e notes 4 2004 80 85

existence of bounded solutions of a class of neutral systems of functional differential equations some results on the existence of bounded solutions together with their first derivatives of a class of neutral systems of functional differential equations with complicated deviations which extend and unify numerous results in the literature are proved

on the system of difference equations x n x n 1 y n 2 a y n 2 b y n 1 y n y n 1 x n 2 c x n 2 d x n 1 we show that the following system of difference equations x n x n 1 y n 2 a y n 2 b y n 1 y n y n 1 x n 2 c x n 2 d x n 1 n n 0 where parameters a b c d as well as initial values x 2 x 1 y 2 y 1 are real numbers is solvable in closed form and by using obtained formulas we give some results on the long term behavior of their solutions we also give natural explanations and considerably extend some recent results in the literature

solutions of a max type system of difference equations we show in an elegant way that the general solution to the following max type system of difference equations xn 1 maxaxn ynxn yn 1 maxayn xnyn n n0 for the case y0 x0 a 0 y0 x0 max a 1 a is given by xn afk n 1 n x0fk n y0fk n 1 n n n y1 x0 y0 and yn y0fk n 1 1afk n 1 n 1x0fk n 1 1 1 n n 2 where k n n for n even k n n 1 for n odd n n0 n n mod2 for n n0 and where the sequence fn n n is the fibonacci sequence correcting and giving a proof of a wrong result in the paper d simsek b demir c cinar on the solutions of the system of difference equations xn 1 max a xn yn xn yn 1 max a yn xn yn discrete dyn nat soc 2009 2009 11 pp article id 325296

lattice boltzmann model for nonlinear convection diffusion equations a lattice boltzmann model for convection diffusion equation with nonlinear convection and isotropic diffusion terms is proposed through selecting equilibrium distribution function properly the model can be applied to the common real and complex valued nonlinear evolutionary equations such as the nonlinear schrodinger equation complex ginzburg landau equation burgers fisher equation nonlinear heat conduction equation and sine gordon equation by using a real and complex valued distribution function and relaxation time detailed simulations of these equations are performed and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies

local existence of lipschitz continuous solutions of systems of nonlinear functional equations with iterated deviations abstract some conditions which guarantee the local existence of lipschitz continuous solutions of some systems of nonlinear functional equations with complicated deviations dependent of unknown functions are presented

a decomposition method for finding solitary and periodic solutions for a coupled higher dimensional burgers equations in this paper we consider coupled higher dimensional burgers chdbur equations we find periodic solutions to chdbur equations using a modified adomian s decomposition method madm we find both exact and numerical solutions we compared the numerical solutions with corresponding analytical solutions we also show the effectiveness of the method

on a symmetric system of max type difference equations we study behavior of positive solutions of the following max type system of difference equationsx n 1 maxc y n px n 1 p y n 1 maxc x n py n 1 p email protected n 0 where p email protected 0 extending some results in the literature among other results we prove that if p email protected 0 1 then every positive solution of the system converges to 1 1

on some periodic systems of max type difference equations we show that all positive solutions to the system of max type difference equations xn 1 max1 i m1f1ixn ki 1 1 1 xn ki 2 1 2 xn ki l 1 l n xn s 1 xn 2 max1 i m2f2ixn ki 1 2 1 xn ki 2 2 2 xn ki l 2 l n xn s 2 xn l max1 i mlflixn ki 1 l 1 xn ki 2 l 2 xn ki l l l n xn s l n n0 where s l mj ki t j n j t 1 l and for a fixed j i 1 mj and where the functions fji 0 l n0 0 j 1 l i 1 mj satisfy some conditions are eventually periodic with not necessarily prime period s a related result for the corresponding system of min type difference equations is also proved

on the system xn 1 ynx n k yn k 1 an bnynxn k yn 1 xnyn k xn k 1 cn dnxnyn k it is shown that the system of difference equationsx n 1 y nx n ky n k 1 a n b ny nx n k y n 1 x ny n kx n k 1 c n d nx ny n k email protected n 0 where email protected n the sequences a n b n c n d n email protected n 0 and the initial values x i y i i 0 email protected are real numbers can be solved in closed form asymptotic behavior of well defined solutions of the system for the case when all the sequences a n b n c n and d n are constant is studied in detail

on difference equations with powers as solutions and their connection with invariant curves abstract we look for nonlinear systems of difference equations which have power functions as solutions and we find a connection to the theory of invariant curves and to self reversed polynomials in particular we construct algebraic solutions of a special equation of invariant curves

existence of bounded solutions of some systems of nonlinear functional differential equations with complicated deviating argument abstract sufficient conditions for the existence of bounded solutions on the real line satisfying lipschitz s condition of a class of systems of nonlinear functional differential equations with complicated deviating argument dependent of unknown functions are given in this paper

part metric and its applications in discrete systems this paper applies the part metric method to study some types of higher order symmetric difference equations with several different exponential parameters these difference equations are proved to have unique equilibria and some useful inequalities regarding the difference equation functions are formulated by use of the part metric and a result given by kruse and nesemann 1999 8 some sufficient conditions on the parameters are given to guarantee the global asymptotic stability of the equilibria furthermore by the part metric defined on matrices this approach is also applicable to show the global asymptotic stability of some cyclic discrete dynamic systems the results of this paper are considered a big improvement over many existing results found in the literature

on a system of difference equations which can be solved in closed form we present an elegant method for solving the system of difference equationsx n 1 1x email protected n y n email protected n 1y n email protected n 0 where parameters a and b and the initial values x 0 and y 0 are positive numbers and by using obtained formulae we show that every solution of the system converges to a two periodic solution

a new lattice boltzmann model for solving the coupled viscous burgers equation abstract in this paper a new lattice boltzmann model for the coupled nonlinear system of viscous burgers equation is proposed by using the double evolutionary equations through selecting equilibrium distribution functions and amending functions properly the governing evolution system can be recovered correctly according to our proposed scheme in which the chapman enskog expansion is employed the effects of space and time resolutions on the accuracy and stability of the model are numerically investigated in detail the numerical solutions for various initial and boundary conditions are calculated and validated against analytic solutions or other numerical solutions reported in previous studies it is found that the numerical results agree well with the analytic solutions which indicates the potential of the present algorithm for solving the coupled nonlinear system of viscous burgers equation

on the system of difference equations xn cnyn 3 an bnyn 1xn 2y n 3 yn γnxn 3 αn βnxn 1yn 2 xn 3 we show that the system of difference equationsx n c ny n 3a n b ny n 1x n 2y n 3 y email protected nx n email protected email protected nx n 1y n 2x n 3 email protected n 0 where the sequences a n b n c n a n b n c n email protected n 0 and initial values x i y i email protected 1 2 3 are real numbers such that c n 0 c n 0 email protected n 0 can be solved in closed form and for the case when all the sequences a n b n c n a n b n and c n are constant we describe the asymptotic behavior of well defined solutions of the system

on a solvable rational system of difference equations abstract we show that the system of difference equations x n 1 x n y n k y n k 1 a n b n x n y n k y n 1 y n x n k x n k 1 c n d n y n x n k n n 0 where k n the sequences a n b n c n d n n n 0 and initial values x i y i i 0 k are real numbers can be solved in closed form by using obtained formulae we investigate asymptotic behavior of well defined solutions of the system for the case when all the sequences a n b n c n and d n are constant

behaviour of solutions of some linear functional equations at infinity relationship between the boundedness and the existence of a finite limit at the infinity of solutions of the linear functional equationx f t email protected t f t where email protected c f r r is a continuous increasing function satisfying the condition f t t email protected r and f is a continuous function such that there is a finite limit lim t f t is studied here by using obtained results we study behaviour of bounded solutions of the functional equationx f k t email protected email protected ix f i t f t where a i i 1 email protected are real numbers such that i 0 k email protected i 1 functions f and f satisfy above mentioned conditions and lim t f t 0

difference equations and nonexistence of solutions of an integral equation abstract by using difference equations we give some easily applicable sufficient conditions for the non existence of nonnegative solutions satisfying some additional conditions of the integral equation f x x a x t b x t f t p d t where p 1 and x is a measurable space with probability measure

infinite alternating groups as finitary linear transformation groups abstract degree of a classical group as its natural projective representation degree see 6 2 case 1 of 2 6 is dispensed with using mal cev s local characterization of finite dimensional linear groups and their classification theorem 2 7 mal cev see 13 l l 91 let g be a iocally finite group with adeg g 00 then g is a finite dimensional linear group theorem 2 8 l 2 8 21 let g be an infinite group then is a simple locally finite linear group of finite degree if and only if g is isomorphic to an adjoint group of lie type over an infinite subfield fp the algebraic closure of f for some prime p 3 local characterization of finitary linear groups a theorem of mal cev type mal cev s theorem 2 7 provides a local characterization of locally finite linear groups g of finite degree the property of having a faithful linear representation of degree n passes from the set of finite subgroups of g to g itself under this section we provide a similar result for locally finite simple groups which are linitary linear remember that the linear transformation g of the vector space i is finitary if g fixes pointwise a subspace of finite codimension in v that is the subspace c g v e v 1 vg v has finite codimension in v or equivalently the subspace v g v g 1 1 v e v has finite dimension in v the collection of all linitary members of gl v forms a normal sub group fgl v and a group which is isomorphic to a subgroup of fgl v for some v is sometimes called a finitary linear group

globally bounded solutions of a system of nonlinear functional differential equations with iterated deviating argument abstract some sufficient conditions which guarantee the existence of a bounded solution together with its first derivative on the whole real line of a system of nonlinear functional differential equations with an iterated deviating argument dependent of unknown function are given

on a nonlinear generalized max type difference equation abstract the boundedness character of positive solutions of the following max type difference equation x n max a x n 1 p x n k r n n 0 where k n 1 the parameters a and r are positive and p is a nonnegative real number is studied in this paper our main results considerably improve results appearing in the literature

dynamics of a family of two dimensional difference systems the boundedness and global asymptotic behavior of positive solutions of the nonlinear two dimensional difference systems x n f x n t 1 y n s 1 y n j y n s 2 x n t 2 where t 1 s 1 s 2 t 2 are all positive integers are investigated some sufficient conditions are established such that the positive solutions converge to the unique equilibrium finally some examples are given to illustrate our results

global stability of a max type difference equation we show that every positive solution to the difference equationx n maxa 1x n p 1 a 1 a 2x n p 2 a 2 a kx n p k a k n n 0 where p i i 1 k are natural numbers such that 1 0 a i 1 1 i 1 k converges to max 1 i ka i 1 a i 1 this result improves and complements the main result in our recent note s stevic global stability of a difference equation with maximum appl math comput 210 2009 525 529 since it also considers the case when a i 1 0 i 1 k

on the recursive sequencexn 1 α xn 1 xn abstract we study the global stability the boundedness character and the periodic nature of the positive solutions of the difference equationxn 1 xn 1 xn where 0 and where the initial conditionsx 1andx0are arbitrary positive real numbers

on a third order system of difference equations abstract we show that the system of difference equations x n 1 a 1 x n 2 b 1 y n z n 1 x n 2 c 1 y n 1 a 2 y n 2 b 2 z n x n 1 y n 2 c 2 z n 1 a 3 z n 2 b 3 x n y n 1 z n 2 c 3 n n 0 where the parameters a i b i c i i 1 2 3 and initial values x j y j z j j 0 1 2 are real numbers can be solved developing further the results in the literature

lattice boltzmann model for high order nonlinear partial differential equations in this paper a general lattice boltzmann lb model is proposed for the high order nonlinear partial differential equation with the form ensuremath partial t ensuremath phi ensuremath sum k 1 m ensuremath alpha k ensuremath partial x k mathrm ensuremath pi k ensuremath phi 0 1 ensuremath le k ensuremath le m ensuremath le 6 ensuremath alpha k are constant coefficients mathrm ensuremath pi k ensuremath phi are some known differential functions of ensuremath phi as some special cases of the high order nonlinear partial differential equation the classical m kdv equation kdv burgers equation mathrm k n n burgers equation kuramoto sivashinsky equation and kawahara equation can be solved by the present lb model compared to the available lb models the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved in addition we also conducted a detailed chapman enskog analysis and found that the high order nonlinear partial differential equation can be correctly recovered from the proposed lb model finally a large number of simulations are performed and it is found that the numerical results agree with the analytical solutions and usually the present model is also more accurate than the existing lb models h lai and c ma sci china ser g 52 1053 2009 h lai and c ma phys a amsterdam 388 1405 2009 for high order nonlinear partial differential equations

trichotomy of a system of two difference equations abstract in this paper we study the boundedness and the asymptotic behavior of the positive solutions of the system of difference equations x n 1 a i 1 k a i x n p i j 1 m b j y n q j y n 1 b i 1 k c i y n p i j 1 m d j x n q j where k m 1 2 a b ai ci bj dj i 1 k j 1 m are positive constants pi qj i 1 k j 1 m are positive integers such that p1

asymptotic behavior of solutions of a system of q functional difference equations abstract the asymptotic behavior and the existence of a bounded lipschitz continuous solution of a system of nonlinear q functional difference equations on a half interval of the real line are studied here the main results compare the behavior of such a solution of the system with bounded solutions of a linear q difference equation

finitary representations and images of transitive finitary permutation groups abstract we characterize the point stabilizers and kernels of finitary permutation representations of infinite transitive groups of finitary permutations moreover the number of such representations is determined

the modified local crank nicolson method for one and two dimensional burgers equations the modified local crank nicolson method is applied to solve one and two dimensional burgers equations new difference schemes that are explicit unconditionally stable and easy to compute are obtained numerical solutions obtained by the present method are compared with exact solutions and it is seen that they are in excellent agreement

on a system of difference equations abstract we show that the system of difference equations x n 1 ax n 1 by n x n 1 c y n 1 y n 1 x n y n 1 n n 0 where the parameters a b c and initial values x 1 x 0 y 1 y 0 are real numbers can be solved considerably improving the results in the literature

periodicity of a class of nonautonomous max type difference equations abstract in this note we prove several general and easily applicable results regarding the periodicity of positive solutions of the following difference equations x n max f 1 x n k 1 n f m x n k m n x n s n n 0 and x n min f 1 x n k 1 n f m x n k m n x n s n n 0 where 1 k 1 k m m s n and where the functions f i 0 n 0 0 1 i m satisfy some additional conditions these results considerably extend and unify numerous results on max type difference equations existing in the literature

a novel lattice boltzmann model for the coupled viscous burgers equations abstract in this work a new lattice boltzmann model for coupled burgers equations is proposed through selecting proper distribution functions unlike the previous models the present model can exactly recover the coupled equations without any assumptions a detailed numerical study on several coupled burgers equations is performed to validate the present model and the results show that the present model not only has a second order convergence rate in space but also is more accurate than the previous model

long term behavior of positive solutions of a system of max type difference equations abstract some sufficient conditions which guaranty the attractivity of all positive solutions of the next system of difference equations x n max a y n 1 p j 2 k x n j q j y n max a x n 1 p j 2 k y n j q j n n 0 where a p 0 and q j j 2 k are nonnegative numbers are given the boundedness character of positive solutions of the system is also studied

a numerical treatment of the coupled viscous burgers equation in the presence of very large reynolds number abstract a numerical investigation of the coupled viscous burgers equation for very large reynolds numbers do not exist in the literature coupled viscous burgers equations are solved numerically in the presence of very large reynolds numbers for this case numerical approach to the coupled viscous burgers equation via contributions of two effective methods is used the first component of the mixed method is finite difference method and the second one is differential quadrature method for this process the third order modified cubic b spline functions are used as base function to display the effectiveness of the present mixed method four different test problems have been investigated for various values of the coefficients more particularly for very large reynolds numbers in other words for the very small value of kinematic viscosity parameters solutions are obtained error norms are calculated and compared with analytical results and also with numerical results of the related literature present results display that the present mixed method obtains high accurate solutions and in compatibility with both of the analytical and numerical results