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

convection diffusion lattice boltzmann scheme for irregular lattices in this paper a lattice boltzmann lb scheme for convection diffusion on irregular lattices is presented which is free of any interpolation or coarse graining step the scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the maxwell boltzmann distribution the axioma holds for both bravais and irregular lattices implying a single framework for lb schemes for all lattice types by solving benchmark problems we have shown that the scheme is indeed consistent with convection diffusion furthermore we have compared the performance of the lb schemes with that of finite difference and finite element schemes the comparison shows that the lb scheme has a similar performance as the one step second order lax wendroff scheme it has little numerical diffusion but has a slight dispersion error by changing the relaxation parameter the dispersion error can be balanced by a small increase of the numerical diffusion

on the steepest descent approximation method for the zeros of generalized accretive operators abstract in this paper we present certain characteristic conditions for the convergence of the generalized steepest descent approximation process to a zero of a generalized strongly accretive operator defined on a uniformly smooth banach space our study is based on an important result of reich s reich an iterative procedure for constructing zeros of accretive sets in banach spaces nonlinear anal 2 1978 85 92 and given results extend and improve some of the earlier results which include the steepest descent approximation method

the solution by iteration of nonlinear equations involving psi strongly accretive operators let e be an arbitrary real banach space and let k c e be a proximal subset of e suppose t k i e is a lipschitz strongly accretive operator such that for any given g e the equation tx f has a solution x e d t it is proved that modified iteration processes of the mann and ishikawa types converge strongly to x related results deal with the solution of the equation x tx f 0 for a strongly accretive or strongly dissipative t and the iterative approximation of fixed points to a strongly pseudocontractive t we also discuss the case where the operator t is only uniformly continuous miramare trieste december 1996 permanent address department of mathematics and computer science nnamdi azikiwe university p m b 5025 awka anambra state nigeria

convergence theorems for strongly pseudo contractive and strongly accretive maps supposeeis an arbitrary real banach space andkis a nonempty closed convex and bounded subset ofe supposet k kis a uniformly continuous strong pseudo contraction with constantk 0 1 suppose an bn cn a n b n and c n are sequences in 0 1 satisfying the following conditions i an bn cn 1 a n b n c n integersn 0 ii lim bn lim b n lim c n 0 iii bn iv cn for arbitraryx0 u0 v0 k define the sequence xn n 0iteratively byxn 1 anxn bntyn cnun yn a nxn b ntxn c nvn n 0 where un vn are arbitrary sequences ink then xn converges strongly to the unique fixed point oft related results deal with the iterative solutions of nonlinear equations involving set valued strongly accretive operators

fixed point theorem for generalized φ pseudocontractive mappings abstract let e be a real banach space c be a nonempty closed convex subset of e and t c c be a continuous generalized pseudocontractive mapping it is proved that t has a unique fixed point in c

lattice boltzmann model for the incompressible navier stokes equation in this paper a lattice boltzmann lb model to simulate incompressible flow is developed the main idea is to explicitly eliminate the terms of o m2 where m is the mach number due to the density fluctuation in the existing lb models in the proposed incompressible lb model the pressure p instead of the mass density is the independent dynamic variable the incompressible navier stokes equations are derived from the incompressible lb model via chapman enskog procedure numerical results of simulations of the plane poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2d womersley flow are presented the numerical results are found to be in excellent agreement with theory

new iteration procedures with errors for multivalued φ strongly pseudocontractive and φ strongly accretive mappings abstract the purpose of this paper is to introduce and study a new class of ishikawa iteration processes with errors for multivalued mappings in real banach spaces some convergence theorems of ishikawa iteration sequences with errors for approximation of the fixed points of multivalued strongly pseudocontractive mappings and approximation of the solutions of nonlinear equations with strongly accretive mappings are obtained respectively our results improve and extend some recent results in this field

on design of a survivable network architecture for dynamic routing optimal solution strategy and an efficient heuristic abstract we investigate network planning and design under volatile conditions of link failures and traffic overload our model is a non simultaneous multi commodity problem with any particular two link failure being considered as one scenario we show that the optimal solution model is not practically solvable for real world problems and hence an efficient heuristic is provided which is o n 6 faster than the optimal model and is based on synthesizing a modified maximum spanning tree using an algorithm due to gomory and hu the output of this procedure is then used to solve a much smaller linear program simulation results indicate that the heuristic is near optimal for problems with up to 40 nodes

iterative solutions of nonlinear accretive operator equations in arbitrary banach spaces suppose e is an arbitrary real banach space and k is a nonempty closed convex and bounded subset of e suppose t k k is a uniformly continuous strong pseudocontraction it is proved that the mann and the ishikawa iteration methods converge strongly to the unique fixed point of t furthermore our results also hold for the slightly more general class of strictly hemicontractive maps related results deal with the iterative approximation of solutions of accretive operator equations in arbitrary real banach spaces miramare trieste april 1996 permanent address department of mathematics university of nigeria nsukka nigeria

approximating fixed points of φ hemicontractive mappings by the ishikawa iteration process with errors in uniformly smooth banach spaces abstract let e be a uniformly smooth banach space and t e e be a continuous and strongly o hemicontractive mapping this paper proves that under suitable conditions the ishikawa iterative sequence with errors strongly converges to the unique fixed point of t the related result deals with the strong convergence of the ishikawa iterative sequence with errors to the unique solution of the equation t x f when t e e is o strongly accretive these results generalize the results of ding 1 into more general o hemicontractive operators and extend a recent paper written by osilike 2 in two ways 1 i the lipschitzian continuity is replaced by the continuity on mapping t 2 ii if the errors u n v n 0 for all n n our theorems of this paper extend results of osilike 2 to the more general class of real uniformly smooth banach spaces

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

iterative processes with mixed errors for nonlinear equations with perturbed m accretive operators in banach spaces let x be a real uniformly smooth banach space of which the dual x has a frechet differentiable norm let a d a x 2 x be an m accretive operator with closed domain d a and bounded range r a and s x x a continuous and a strongly accretive operator with bounded range r i s it is proved that the ishikawa and mann iterative processes with mixed errors converge strongly to the unique solution of the equation z sx lax for given z x and l 0

convergence of iterative processes with errors for set valued pseudocontractive and accretive type mappings in banach spaces abstract in this paper some new results on convergence of iterative processes with errors for set valued pseudocontractive and accretive mappings in banach spaces are obtained our results extend and improve a number of the recent results

general bounce back scheme for concentration boundary condition in the lattice boltzmann method in this paper a general bounce back scheme is proposed to implement concentration or thermal boundary conditions of convection diffusion equation with the lattice boltzmann method lbm using this scheme the general concentration boundary conditions i e b 1 frac ensuremath partial c w ensuremath partial n b 2 c w b 3 can be easily implemented at boundaries with complex geometry structure like that in porous media the numerical results obtained using the present scheme are in excellent agreement with the analytical solutions of flows with both stationary and moving interfaces furthermore to better understand the halfway bounce back scheme an analytical study of the concentration jump is presented the studies of theoretical analysis and numerical experiments demonstrate that the proposed scheme has second order accuracy

a generalized steepest descent approximation for the zeros of m accretive operators a necessary and sufficient condition is proved for a generalized steepest descent approximation to converge to the zeros of m accretive operators related results deal with the convergence of the scheme to fixed points of pseudocontractive maps

an iterative algorithm for approximating solutions of hammerstein equations with monotone maps in banach spaces abstract let e l p 1 u k f u 0 has a solution u a coupled iterative process is constructed and proved to converge strongly to u furthermore our technique of proof is of independent interest

iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo contractive mappings in banach spaces abstract in this article we prove some new convergence theorems of the ishikawa and mann iteration sequences for strongly accretive and strongly pseudo contractive mappings by using the new inequality and the new approximation methods our main results improve and extend the corresponding results of j math anal appl 151 1990 453 461 proc amer math soc 120 1994 545 551 j math appl 192 1995 502 518 j math anal appl 174 1993 441 449 acta appl math 32 1993 183 196 nonlinear anal tma 24 1995 981 987 j math anal appl 178 1993 9 21 proc amer math soc 125 6 1997 1705 1709

perturbed iterative process for fixed points of multivalued φ hemicontractive mappings in banach spaces abstract in this paper the unique fixed point of multivalued hemicontractive mapping is approximated by a perturbed iteration method in arbitrary real banach spaces

an improved lattice boltzmann method for simulating advective diffusive processes in fluids abstract lattice boltzmann methods are widely used to simulate advective diffusive processes in fluids lattice bhatnagar gross krook methods presented in the literature mostly just exhibit first order spatial accuracy and introduce errors proportional to the velocity squared formulations proposed to alleviate this have only been partly successful and are valid only in certain specific situations we present and demonstrate here a formulation that produces no such second order errors this formulation suggests that a subtle but important adjustment is all it takes to improve the accuracy of the method the key to the improved accuracy of this new model is the non standard definition of the concentration that relates to the distribution function describing the advection diffusion in lattice boltzmann the main advantage of the algorithm comes to view when simulating situations where fluid density variations appear the present formulation of the advection diffusion algorithm will by taking into account these fluid density variations drastically reduce the errors produced compared to the standard formulations we also show how a source term is included in this new formulation without it losing its second order spatial accuracy

a multi relaxation lattice kinetic method for passive scalar diffusion a kinetic lattice boltzmann scheme for advection diffusion is presented the scheme is based on a matrix formulation of the lattice boltzmann method which permits to handle non isotropic diffusion advection problems in addition by adjusting the kinetic eigenvectors defining the collision matrix to the local value of the flow velocity the scheme is also shown to preserve isotropy under genuinely two dimensional flow

discrete lattice effects on the forcing term in the lattice boltzmann method we show that discrete lattice effects must be considered in the introduction of a force into the lattice boltzmann equation a representation of the forcing term is then proposed with the representation the navier stokes equation is derived from the lattice boltzmann equation through the chapman enskog expansion several other existing force treatments are also examined

on φ strongly accretive mappings and some set valued variational problems abstract this paper shows that a continuous strongly accretive mapping on a real banach space is single valued and some recent results of set valued variational inclusions and inequalities are discussed

the solution by iteration of nonlinear equations in uniformly smooth banach spaces abstract letebe a uniformly smooth banach space and lett d t e ebe a strong pseudocontraction with an open domaind t ineand a fixed pointx d t we establish the strong convergence of the mann and ishikawa iterative processes with errors to the fixed point oft related results deal with the iterative solution of operator equations of the formsf txandf x tx 0 whentis a set valued strongly accretative operator our theorems include the cases in which the operatortis defined only locally explicit error estimates are also given

a new scheme for source term in lbgk model for convection diffusion equation a new scheme for source term in the lattice bgk lbgk model for convection diffusion equation is proposed unlike the models proposed previously the present scheme only requires the source term in order of the knudsen number by adding a differential operator of the source term to the evolution equation the scheme can be applied to reaction diffusion systems directly numerical results are found to be in excellent agreement with the analytical solutions it is also found that the numerical accuracy of the present scheme is generally much better than that of the existing models

iteration processes for nonlinear lipschitzian strongly accretive mappings in lp spaces abstract suppose x l p or l p 1 p 2 let t x x be a lipschitzian and strongly accretive map with constant k 0 1 and lipschitz constant l satisfying p p 1 l 2 p 2 p 1 1 k define s x x by sx tx x for arbitrary x 0 x the sequence x n n 1 is defined by x n 1 1 n x n n sy n y n 1 n x n n sx n n 0 where n n 1 n n 1 are two real sequences satisfying i 0 n 2 1 p 2 p 1 1 k k n l 2 n p 2 p l 2 1 w n w l 2 1 2 n p 2 p 1 1 k k n l 2 n p 1 2 l 2 1 w n w l 2 1 2 n 1 1 for each n ii 0 n min w w l 2 1 1 w 4 p 1 l 2 k p 1 2 l 2 w 1 for each n iii n n where w p 2 p 1 1 k p 2 p l 2 then x n 1 converges strongly to the unique solution of tx moreover if n 2 1 p 2 p 1 1 k k l 2 p 2 p l 2 1 w w l 2 1 2 p 2 p 1 1 k k l 2 p 1 2 l 2 1 w w l 2 1 2 1 1 and n for each n and some 0 min w w l 2 1 1 w 4 p 1 l 2 k p 1 2 l 2 w 1 then x n 1 q p n 2 x 1 q where q denotes the solution of tx and 1 4 1 p 2 p 1 1 k k l 2 p 2 p l 2 1 w w l 2 1 2 2 p 2 p 1 1 k k l 2 p 1 2 l 2 1 w w l 2 1 2 1 1 0 1 a related result details with the iterative approximation of lipschitz strongly pseudocontractive maps in x

accretive operators which are always single valued in normed spaces abstract set valued accretive operators in banach spaces have been extensively studied for several decades our main purpose in this paper is to establish a quite revealing result that says that every set valued lower semi continuous accretive mapping defined on a normed space is indeed single valued on the interior of its domain no reference to the well known michael s selection theorem is needed this result is used to extend known theorems concerning the existence of zeros for such operators as well as showing existence of solutions for variational inclusions

the solution by iteration of nonlinear equations of hammerstein type let e be a real uniformly smooth banach space suppose n is a set valued locally accretive map with open domain d n c e k is a single valued map with domain d k c e such that im n c d k and k exists and is locally strongly accretive on im k if the equation f e x knx has a solution x e d n the strong convergence of iteration methods of the ishikawa and mann types to this solution is established related theorems deal with the iterative solution of nonlinear equations of the form f g x tx for the case where t is accretive explicit convergence rates are established miramare trieste november 1996 permanent address department of mathematics and computer science nnamdi azikiwe university p m b 5025 awka anambra state nigeria

iterative solution of nonlinear equations with strongly accretive operators abstract let e be a real banach space with a uniformly convex dual suppose t e e is a strongly accretive map with bounded range such that for each e the equation tx has a solution in e it is proved that each of the two well known fixed point iteration methods the mann and ishikawa iteration methods under suitable conditions converges strongly to a solution of the equation tx furthermore our method shows that such a solution is necessarily unique explicit error estimates are given our results resolve in the affirmative an open problem j math anal appl 151 no 2 1990 460 and generalize important known results

iterative solutions of nonlinear equations with φ strongly accretive operators in uniformly smooth banach spaces abstract suppose that x is a uniformly smooth banach space and t x x is a demicontinuous not necessarily lipschitz strongly accretive operator it is proved that the ishikawa iterative method with errors converges strongly to the solutions of the equations f tx and f x tx respectively a related result deals with the approximation of fixed points of strongly pseudocontractive operators our results extend improve and unify the recent results obtained by chidume 1 2 and zhou 3

viscosity approximation methods for pseudo contractive semigroups in banach spaces abstract we study the strong convergence of two viscosity iteration processes for pseudo contractive semigroup and for strongly pseudo contractive mapping in uniformly convex banach spaces with uniformly g teaux differentiable norm as special cases we get strong convergence of two viscosity iteration processes for approximating common fixed points of nonexpansive semigroups in certain banach spaces the results presented in this paper extend and generalize previous results

analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice boltzmann bgk model in this paper we analytically solve the velocity of the lattice boltzmann bgk equation lbgk for several simple flows the analysis provides a framework to theoretically analyze various boundary conditions in particular the analysis is used to derive the slip velocities generated by various schemes for the nonslip boundary condition we find that the slip velocity is zero as long as f e 0 at boundaries no matter what combination of distributions is chosen the schemes proposed by nobleet al and by inamuroet al yield the correct zeroslip velocity while some other schemes such as the bounce back scheme and the equilibrium distribution scheme would inevitably generate a nonzero slip velocity the bounce back scheme with the wall located halfway between a flow node and a bounce back node is also studied for the simple flows considered and is shown to produce results of second order accuracy the momentum exchange at boundaries seems to be highly related to the slip velocity at boundaries to be specific the slip velocity is zero only when the momentum dissipated by boundaries is equal to the stress provided by fluids

a perturbed iterative procedure for multivalued pseudo contractive mappings and multivalued accretive mappings in banach spaces abstract the main purpose of this paper is to introduce and study a new perturbed iteration method for multivalued mappings some strong convergence theorems of perturbed iteration sequences for multivalued pseudo contractive mappings and strongly accretive mappings are obtained

accumulation and control of random errors in the ishikawa iterative process in arbitrary banach space the purpose of this note is to study directly the relation between random errors and two parameter sequences in the ishikawa iterative process and to estimate the accumulation of errors in the iterative process the obtained results show that when one of the sequences converges to zero the accumulation of errors is bounded if the other sequence is non summable while the accumulation of errors is controllable in a permissible range if the sequence is summable

nonequilibrium scheme for computing the flux of the convection diffusion equation in the framework of the lattice boltzmann method in this paper we propose a local nonequilibrium scheme for computing the flux of the convection diffusion equation with a source term in the framework of the multiple relaxation time mrt lattice boltzmann method lbm both the chapman enskog analysis and the numerical results show that at the diffusive scaling the present nonequilibrium scheme has a second order convergence rate in space a comparison between the nonequilibriumschemeandtheconventionalsecond ordercentral differenceschemeindicatesthat althoughboth schemes have a second order convergence rate in space the present nonequilibrium scheme is more accurate than thecentral differencescheme inaddition thefluxcomputationrenderedbythepresentschemealsopreservesthe parallel computation feature of the lbm making the scheme more efficient than conventional finite difference schemes in the study of large scale problems finally a comparison between the single relaxation time model and the mrt model is also conducted and the results show that the mrt model is more accurate than the single relaxation time model both in solving the convection diffusion equation and in computing the flux

effect of the forcing term in the multiple relaxation time lattice boltzmann equation on the shear stress or the strain rate tensor in this work the effect of the forcing term or external force in the multiple relaxation time lattice boltzmann equation mrtlbe on the shear stress or the strain rate tensor is studied theoretically and numerically through a chapman enskog analysis and numerical simulations we show that the shear stress or the strain rate tensor derived from the mrtlbe is second order accurate in space we then examine the influence of the forcing term on the shear stress or the strain rate tensor and demonstrate that the forcing term effect must be included when the shear stress or the strain rate tensor is computed with the nonequilibrium part of the distribution function

ishikawa iteration process for nonlinear lipschitz strongly accretive mappings abstract let e lp p 2 and let t e e be a lipschitzian and strongly accretive mapping let s e e be defined by sx tx x it is proved that under suitable conditions on the real sequences n n 0 and n n 0 the iteration process x0 e xn 1 1 n xn ns 1 n xn nsxn n 0 converges strongly to the unique solution of tx a related result deals with the iterative approximation of fixed points for lipschitz strongly pseudocontractive mappings in e a consequence of our result gives an affirmative answer to a problem posed by c e chidume j math anal appl 151 no 2 1990 453 461

convergence theorems for φ strongly accretive and φ hemicontractive operators suppose that x is an arbitrary real banach space and t x x is a continuous strongly accretive operator it is shown that the nonlinear equation tx f has a unique solution and under certain conditions both the mann and ishikawa iteration methods with errors introduced by y xu 1998 j math anal appl 224 91 101 converge strongly to the solution a related result deals with the approximation of fixed points of hemicontractive operators

lattice bgk model for incompressible navier stokes equation abstract most of the existing lattice boltzmann bgk models lbgk can be viewed as compressible schemes to simulate incompressible fluid flows the compressible effect might lead to some undesirable errors in numerical simulations in this paper a lbgk model without compressible effect is designed for simulating incompressible flows the incompressible navier stokes equations are exactly recovered from this incompressible lbgk model numerical simulations of the plane poiseuille flow the unsteady 2 d shear decaying flow the driven cavity flow and the flow around a circular cylinder are performed the results agree well with the analytic solutions and the results of previous studies

steepest descent method for equilibrium points of nonlinear systems with accretive operators let e be a real normed linear space and let a e 2e be a bounded uniformly continuous strongly accretive multi valued map with nonempty closed values such that the inclusion 0 ax has a solution x e it is proved that both the ishikawa and the mann iteration processes are bounded and converge strongly to x related results deal with the convergence of the iteration processes to fixed points of strongly pseudocontractive maps and the iterative solution of the equation 0 x fx for an accretive map f furthermore the ishikawa and mann iteration methods with errors are discussed and proofs are sketched on how our theorems extend to these methods our method of proof is of independent interest

iterative solution of nonlinear equations involving strongly accretive operators without the lipschitz assumption abstract letebe a real banach space with a uniformly convex dual spacee supposet e eis a continuous not necessarily lipschitzian strongly accretive map such that i t has bounded range whereidenotes the identity operator it is proved that the ishikawa iterative sequence converges strongly to the unique solution of equationtx f f e our results extend and complement the recent results obtained by chidume

multiple relaxation time lattice boltzmann model for the convection and anisotropic diffusion equation a lattice boltzmann model with a multiple relaxation time mrt collision operator for the convection diffusion equation is presented the model uses seven discrete velocities in three dimensions d3q7 model the off diagonal components of the relaxation time matrix which originate from the rotation of the principal axes enable us to take into account full anisotropy of diffusion an asymptotic analysis of the model equation with boundary rules for the dirichlet and neumann type specified flux conditions is carried out to show that the model is first and second order accurate in time and space respectively the results of the analysis are verified by several numerical examples it is also shown numerically that the error of the mrt model is less sensitive to the variation of the relaxation time coefficients than that of the classical bgk model in addition an alternative treatment for the neumann type boundary condition that improves the accuracy on a curved boundary is presented along with a numerical example of a spherical boundary

on stability results for φ strongly pseudocontractive mappings abstract we study the stability problems of the following unified iterative scheme involving a strongly pseudocontractive mapping or hemicontractive mapping t x n 1 f t v n x n n x n n tv n n u n in arbitrary banach spaces we apply our results to obtain stability of an iterative scheme for a family of k selfmappings

convergence theorem for the common solution for a finite family of ϕ strongly accretive operator equations the purpose of this paper is to study a strong convergence of multi step iterative scheme to a common solution for a finite family of uniformly continuous strongly accretive operator equations in an arbitrary banach space as a consequence the strong convergence theorem for the multi step iterative sequence to a common fixed point for finite family of strongly pseudocontractive mappings is also obtained the results presented in this paper thus improve and extend the corresponding results of inchan 6 kang 8 9 and many others

an iterative process for nonlinear lipschitzian strongly accretive mappings in lp spaces abstract suppose x l p or l p p 2 let t x x be a lipschitzian and strongly accretive map with constant k 0 1 and lipschitz constant l define s x x by sx f tx x let c n n 1 be a real sequence satisfying 1 i 0 c n k p 1 l 2 2 k 1 1 for each n 2 ii n c n then for arbitrary x 0 x the sequence x n 1 1 c n x n c n sx n n 0 converges strongly to the unique solution of tx f moreover if c n k p 1 l 2 2 k 1 1 for each n then x n 1 q n 2 x 1 q where q denotes the solution of tx f and 1 k p 1 l 2 2 k 1 1 0 1 a related result deals with the iterative approximation of lipschitz strongly pseudocontractive maps in x

the multi terminal maximum flow network interdiction problem abstract this paper defines and studies the multi terminal maximum flow network interdiction problem mtnip in which a network user attempts to maximize flow in a network among k 3 pre specified node groups while an interdictor uses limited resources to interdict network arcs to minimize this maximum flow the paper proposes an exact mtnip e and an approximating model mpnim to solve this np hard problem and presents computational results to compare the models mtnip e is obtained by first formulating mtnip as bi level min max program and then converting it into a mixed integer program where the flow is explicitly minimized mpnim is binary integer program that does not minimize the flow directly it partitions the node set into disjoint subsets such that each node group is in a different subset and minimizes the sum of the arc capacities crossing between different subsets computational results show that mpnim can solve all instances in a few seconds while mtnip e cannot solve about one third of the problems in 24 hour the optimal objective function values of both models are equal to each other for some problems while they differ from each other as much as 46 2 in the worst case however when the post interdiction flow capacity incurred by the solution of mpnim is computed and compared to the objective value of mtnip e the largest difference is only 7 90 implying that mpnim may be a very good approximation to mtnip e

on chidume s open questions and approximate solutions of multivalued strongly accretive mapping equations in banach spaces abstract some new convergence theorems of the ishikawa iteration process for multi valued pseudo contractive mappings and multi valued accretive mappings are obtained which affirmatively answer the open questions put forth by 4

ishikawa and mann iteration methods with errors for nonlinear equations of the accretive type abstract let e be an arbitrary banach space and t e e a lipschitz strongly accretive operator it is proved that for a given f e the ishikawa and the mann iteration methods with errors introduced by 18 converge strongly to the solution of the equation tx f furthermore if e is a uniformly smooth banach space and t e e is demicontinuous and strongly accretive it is also proved that both the ishikawa and the mann iteration methods with errors converge strongly to the solution of the equation tx f related results deal with the iterative approximation of fixed points of strongly pseudocontractive operators and the solution of the equation x tx f f e when t e e is m accretive

lattice boltzmann models for two dimensional coupled burgers equations abstract in this paper two lattice boltzmann models for two dimensional coupled burgers equations are proposed through treating the part or all of convection items as the source term where the spatial gradient can be calculated by the distribution function the models can exactly recover the burgers equations without any assumptions some numerical tests are also performed to validate the present models it is found that the proposed models are more accurate and efficient in solving two dimensional coupled burgers equations

stable iteration procedures for strong pseudocontractions and nonlinear equations involving accretive operators without lipschitz assumption abstract let e be a real uniformly smooth banach space and t e e a strong pseudocontraction with a bounded range we prove that the mann and ishikawa iteration procedures are t stable some related results deal with the stability of these procedures for the iteration approximation of solutions of nonlinear equations involving accretive operators our results improve and or extend those corresponding results announced by osilike

steepest descent approximations for accretive operator equations a necessary and sufficient condition is established for the strong convergence of the steepest descent approximation to a solution of equations involving quasi accretive operators defined on a uniformly smooth banach space miramare trieste march 1993

numerical study of lattice boltzmann methods for a convection diffusion equation coupled with navier stokes equations numerous lattice boltzmann lb methods have been proposed for solution of the convection diffusion equations cde for the 2d problem d2q9 d2q5 or d2q4 velocity models are usually used when lb convection diffusion models are used to solve a cde coupled with navier stokes equations boundary conditions are found to be critically important for accurately solving the coupled simulations following the idea of a regularized scheme latt et al 2008 phys rev e 77 056703 a regularized boundary condition for solving a cde is proposed a simple extrapolation scheme is also proposed for the neumann boundary condition spatial accuracies of three existing and the proposed boundary conditions are discussed in details the numerical evaluations are based on simulations of steady and unsteady natural convection flows in a cavity and an unsteady taylor couette flow our studies show that the simplest d2q4 model with terms of o u in the equilibrium distribution function is capable of obtaining results of equal accuracy as d2q5 or d2q9 models for the cde a slightly revised lb equation for solving a cde that is used to cancel some unwanted terms does not seem to be necessary for incompressible flows the regularized boundary condition for solving the cde has second order spatial accuracy and it is the best one in terms of the spatial accuracy the regularized scheme and non equilibrium extrapolation scheme are applicable to handle both the dirichlet and neumann boundary conditions for the neumann boundary condition with zero flux all the five boundary conditions are applicable to give accurate results and the bounce back scheme is the simplest one

iterative solution of nonlinear equations of the φ strongly accretive type abstract letq 1 and letebe a realq uniformly smooth banach space lett e ebe a lipschitz strongly accretive operator and suppose the equationtx f f e has a solution it is proved that under suitable conditions on the real sequences n n 0 and n n 0 the iteration process formula converges strongly to the unique solution of the equationtx f a related result deals with the approximation of fixed points of hemicontractive operators a class of operators which is much more general than the important class of strongly pseudocontractive operators

the exact solution of nonlinear operator equation aubu cu f abstract this paper is intended to discuss the problems of solving system of linear operator equations and a kind of nonlinear operator equation a u b u c u f for system of linear operator equations we obtain a criterion about the existence of solutions if it has solutions we get the analytic representation of its minimum norm solution and the structure of its solution space for nonlinear operator equation a u b u c u f with the help of the discussion on how to solve the system of linear operator equations the exact solution is given besides we obtain the representation of all its solutions

ishikawa and mann iterative processes with errors for nonlinear strongly accretive operator equations abstract the purpose of this paper is to revise the definitions of ishikawa and mann iterative processes with errors by using a new inequality to study the unique solution of the nonlinear strongly accretive operator equationtx fand the convergence problem of ishikawa and mann iterative sequences for strongly pseudo contractive mappings without the lipschitz condition the results presented in this paper improve and extend the corresponding results in 4 5 7 10 12 15 16 in the more general setting in particular the open problem mentioned by chidume in 5 has been given an affirmative answer

global existence and mann iterative algorithms of positive solutions for first order nonlinear neutral delay differential equations abstract this paper deals with the first order nonlinear neutral delay differential equation d dt x t p t x t f t x 1 t x 2 t x n t 0 t t 0 where 0 p c t 0 r f c t 0 r n r and l c t 0 r with limt l t for l 1 2 n by using the banach fixed point theorem we prove the global existence of uncountably many bounded positive solutions for the above equation relative to all ranges of the function p construct some mann type iterative algorithms with errors to approximate these positive solutions and discuss several error estimates between the sequences generated by the iterative algorithms and these positive solutions seven examples are presented to illuminate the results obtained in this paper

polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems we show that a particular pivoting algorithm which we call the lexicographic lemke algorithm takes an expected number of steps that is bounded by a quadratic inn when applied to a random linear complementarity problem of dimensionn we present two probabilistic models both requiring some nondegeneracy and sign invariance properties the second distribution is concerned with linear complementarity problems that arise from linear programming in this case we give bounds that are quadratic in the smaller of the two dimensions of the linear programming problem and independent of the larger similar results have been obtained by adler and megiddo

iterative process with errors to nonlinear ф strongly accretive operator equations in arbitrary banach spaces abstract let x be an arbitrary banach space and t d t x x be a lipschitz strongly accretive operator with domain d t and range r t the mann and ishikawa type iterative sequences with errors which strongly converge to the unique solution of the equation tx f under weaker conditions are given the related results deal with the problems that the mann and ishikawa iterative sequences with errors strongly converge to the unique fixed point of lipschitz hemicontractive operators

another note on a paper convergence theorem for the common solution for a finite family of φ strongly accretive operator equations in this paper we first point out a gap in yang 2012 next strong convergence theorem for the common solution for a finite family of strongly accretive operator equations in banach spaces is established without any bounded assumption and we also give an example to show universality of the result of this paper which improve and extend some recent results

iterative process with errors for fixed points of multivalued φ hemicontractive operators in uniformly smooth banach spaces abstract let e be a uniformly smooth banach space and t e 2e be a not necessarily continuous multivalued o hemicontractive mapping this paper proves that under suitable conditions the multivalued ishikawa iterative sequence with errors strongly converges to the unique fixed point of t the related result deals with the strong convergence of the ishikawa iterative sequence with errors to the unique solution of the equation f tx when t e 2e is multivalued o strongly accretive these results generalize the results of the author 1 ding 2 3 osilike 4 5 zhou 6 7 and chidume 8 9 into more general multivalued o hemicontractive operators without the continuous assumption on operators t