a class of bidiagonal schemes for solving the euler equations a class of implicit bidiagonal schemes is developed for the conservative euler equations the schemes are based on a predictor corrector approach for the characteristic variables adapted according to the sign of the characteristic speeds of information they are second order accurate in space and time and have intrinsic dissipative properties a new fully implicit boundary treatment is developed for this class of schemes allowing high cfl numbers in all regions of the flow domain results are presented for the quasi one dimensional flow in a nozzle n recent years substantial progress has been made in the development of numerical methods for solving conservative systems of hyperbolic equations such as the euler equations describing inviscid fluid flow m one of the main achievements has been the development of implicit methods based on tridiagonal solution procedures 2 the use of explicit impl icit artificial viscosity5 and of implicit boundary conditions6 7 has made these algorithms very robust and efficient recently an implicit method based on a bidiagonal solution technique has been introduced by maccormack 1 the first part of this paper is concerned with further developments related to the bidiagonal solution technique a general class of second order accurate bidiagonal schemes is proposed containing a class of implicit schemes and one of semiexplicit schemes it is shown that these schemes are in trinsically dissipative so that no artificial viscosity is necessary for linear stability the second part of the paper introduces an implicit boundary treatment for these bidiagonal schemes that preserves the stability properties of the interior scheme in deed while a number of successful boundary procedures have been proposed for explicit and tridiagonal implicit schemes this stability remained an unsolved problem in earlier ap plications of bidiagonal techniques 8 9 numerical experiments for the euler flow in a nozzle confirm the unconditional linear stability allowing the use of very high cfl numbers

an implicit bidiagonal numerical method for solving the navier stokes equations in recent years much progress has been made in solving fluid dynamical problems using finite difference methods solving inviscid compressible problems in two and three dimensions has become almost routine with many suitable methods explicit or implicit available the problem of compressible viscous flows in complicated geometries remains however a major challenge here fine mesh spacing in the viscous flow regions makes the explicit methods with their simple boundary conditions extremely costly existing implicit methods can make use of large time steps but require inversions of large block tridiagonal matrices a method recently developed by maccormack eliminates this disadvantage by introducing a predictor corrector scheme requiring the inversion of only block bidiagonal matrices it is the aim of present work to extend this method to allow solution of viscous compressible problems in general coordinates for arbitrary two dimensional geometries

fixed points of weak contractions in cone metric spaces abstract cone metric spaces are generalizations of metric spaces where the metric is banach space valued weak contractions are generalizations of the banach s contraction mapping which have been studied by several authors in the present work we establish a unique fixed point result for weak contractions in cone metric spaces our result is supported by an example

coincidence and common fixed point theorems for a sequence of mappings in ordered metric spaces in this article the existence of coincidence points and common fixed points for a sequence of mappings satisfying generalized weakly contractive conditions which involves altering distance functions without exploiting the notion of continuity of any map involved therein in a ordered metric space is proved an example is given to support the usability of our results

existence of solutions to fuzzy differential equations with generalized hukuhara derivative via contractive like mapping principles abstract we study the existence and uniqueness of solution for fuzzy initial value problems in the setting of a generalized hukuhara derivative and by using some recent results of fixed point of weakly contractive mappings on partially ordered sets

a generalized contraction principle with control functions on partial metric spaces partial metric spaces were introduced by matthews in 1994 as a part of the study of denotational semantics of data flow networks in this article we prove a generalized contraction principle with control functions f and j on partial metric spaces the theorems we prove generalize many previously obtained results we also give some examples showing that our theorems are indeed proper extensions

reply by authors to g degrez references 1 casier f deconinck h and hirsch ch a class of bidiagonal schemes for solving the euler equations aiaa journal vol 22 nov 1984 pp 1556 1563 2 maccormack r w the effect of viscosity in hypervelocity impact cratering aiaa paper 69 354 april 1969 3 maccormack r w a numerical method for solving the equations of compressible viscous flow aiaa journal vol 20 sept 1982 pp 1275 1281

iterative selection methods for the common fixed point problems in a banach space many problems encountered in applied mathematics can be recast as the problem of selecting a particular common fixed point of a countable family of non expansive mappings in banach space in the paper under the hypotheses that e is a reflexive banach space which has a weakly continuous duality mapping j with gauge function several viscosity approximation methods are investigated for finding a common fixed point of non expansive mapping sequences

coincidence and fixed point theorems for generalized ψ φ weak nonlinear contraction in ordered k metric spaces in this paper we establish coincidence and fixed point theorems for a pair of mappings satisfying a new generalized j f weak nonlinear contraction type condition in ordered k metric spaces the presented results generalize and extend the very recent results of choudhury and metiya b s choudhury and n metiya the point of coincidence and common fixed point for a pair of mappings in cone metric spaces computers and mathematics with applications 60 2010 1686 1695

fixed point theorems for nonlinear contractions in kaleva seikkala s type fuzzy metric spaces in this paper the existence and unicity of fixed points for mappings in fuzzy metric spaces in the sense of kaleva and seikkala is discussed nonlinear contractions of the boyd wong s type alber guerre delabriere s type and kannan reich s type are considered and several new fixed point theorems for these contractions in complete fuzzy metric spaces are presented respectively also some error estimates are given for iterations to approximate fixed point previous work with respect to fixed point in fuzzy metric spaces is based on the t conorm max the presented work does away with this restriction by proposing weaker conditions defining a generic class of suitable binary operations as applications the corresponding fixed point theorems for menger probabilistic metric spaces are obtained

almost periodicity of set valued functions and set dynamic equations on time scales in this paper we first propose the concept of the almost periodicity of set valued functions on almost periodic time scales then based on the exponential dichotomy we discuss the existence and uniqueness of almost periodic solutions of set dynamic equations on time scales as an application several examples are presented to exhibit that one can obtain the existence of almost periodic solutions to interval valued dynamic equations or fuzzy dynamic equations and their discrete counterparts in a united means

fixed point theorems for generalized weakly contractive mappings we prove a fixed point theorem for a generalized weakly contractive mapping and a fixed point theorem for a pair of weakly contractive mappings we also show that these mappings satisfy properties p and q

some common fixed point theorems for generalized nonlinear contractive mappings sufficient conditions for the existence of a common fixed point for generalized nonlinear contractive mappings are derived as applications some results on the set of best approximation for this class of mappings are also obtained the proved results generalize and extend various known results in the literature

generalized weak contractions in partially ordered metric spaces recent results of doric d doric common fixed point for generalized j f weak contractions appl math lett 22 2009 1896 1900 on generalized weakly contractive mappings are extended to the setting of partially ordered metric spaces thus generalization of fixed point results of harjani and sadarangani j harjani k sadarangani fixed point theorems for weakly contractive mappings in partially ordered sets nonlinear anal 71 2009 3403 3410 is obtained some applications are presented examples are given to show that our results are proper generalizations of the existing ones

fixed point results for cyclic α ψ φ contractions with application to integral equations in this paper we introduce the notions of contractive and cyclic contractive mappings and establish the existence and uniqueness of fixed points for such mappings in complete metric like spaces the results presented here substantially generalize and extend several comparable results in the existing literature in particular those of karapinar and salimi 2013 as an application we prove new fixed point results for graphic and cyclic graphic contractive mappings moreover some examples and an application to integral equations are given here to illustrate the usability of the obtained results

existence and uniqueness of common fixed points for two multivalued operators in ordered metric spaces in this paper we discuss some new fixed point theorems for a pair of multivalued operators which satisfy weakly generalized contractive conditions our results are the extension and improvement of corresponding results of j harjani and k sadarangani fixed point theorems for weakly contractive mappings in partially ordered sets nonlinear analysis 71 2009 3403 3410 and x zhang common fixed point theorems for some new generalized contractive type mappings j math anal appl 333 2007 780 786 finally some examples are given to illustrate the usability of our results

common fixed points of almost generalized contractive mappings in ordered metric spaces the existence theorems of common fixed points for two weakly increasing mappings satisfying an almost generalized contractive condition in ordered metric spaces are proved some comparative example are constructed which illustrate the values of the obtained results in comparison to some of the existing ones in literature

existence of the solution to variational inequality optimization problem and elliptic boundary value problem through revisited best proximity point results abstract in this paper we establish some results regarding the existence of the solution to variational inequality optimization problem and elliptic boundary value problem in hilbert spaces our strategy consists in establishing new best proximity point results in the metric spaces by introducing the concept of cyclic orbital simulative contractions we also provide nontrivial examples to show that our results are proper generalization further we improve the recent best proximity results for mappings satisfying proximal simulative conditions due to abbas et al 2017 samet 2015 and tchier et al 2016 via new class of simulation functions our results unify extend and generalize various existing results

viscosity approximation schemes for fixed point problems and equilibrium problems and variational inequality problems abstract in this paper we first introduce a general iterative scheme by halpern approximation method for finding a common element of the set of solutions of an equilibrium problem the set of solutions of the variational inequality for an infinite family of i inverse strongly monotone mappings and the set of common fixed points for a family of infinitely nonexpansive mappings in a hilbert space then we extend the halpern iterative scheme to a general viscosity approximation scheme by a simple and different method as applications we utilize our results to investigate some convergence problems for strictly pseudocontractive mappings and maximal monotone operators the results obtained in this paper extend and improve the recent ones announced by many others

best proximity point theorems an exploration of a common solution to approximation and optimization problems abstract given a non self mapping t a b in the setting of a metric space this work concentrates on the resolution of the non linear programming problem of globally minimizing the real valued function x d x tx thereby yielding an optimal approximate solution to the equation tx x an iterative algorithm is also presented to compute a solution of such problems as a sequel it is possible to compute an optimal approximate solution to some non linear equations

coincidence point theorem for generalized weakly contractions in ordered metric spaces abstract in this article we establish two coincidence point theorems for four mappings satisfying a generalized weakly contractive condition in ordered metric space and apply it to find new coincidence point and common fixed point results we furnish suitable examples to demonstrate the validity of the hypotheses of our results also we give an existence theorem for common solution of two integral equations

solving variational inequalities involving nonexpansive type mappings abstract the purpose of this paper is to investigate the asymptotic behavior of algorithms for finding solutions for a certain class of variational inequalities v i d c i f involving nonexpansive type mappings in smooth banach spaces we study the existence of solutions of variational inequalities v i d c i f when d is the set of solutions of zeros of accretive operators or the set of fixed points of nonexpansive mappings or the set of fixed points of pseudocontractive mappings our convergence analysis covers proximal point algorithm for finding zeros of accretive operators as well as functional halpern algorithm for finding fixed points of nonexpansive mappings in banach spaces our results improve a number of results concerned with viscosity approximation methods in the context of weakly contraction mappings

semiclassical transition from an elliptical to an oval billiard semiclassical approximations often involve the use of stationary phase approximations this method can be applied when is small in comparison with relevant actions or action differences in the corresponding classical system in many situations however action differences can be arbitrarily small and then uniform approximations are more appropriate in this paper we examine different uniform approximations for describing the spectra of integrable systems and systems with mixed phase space this is done on the example of two billiard systems an elliptical billiard and a deformation of it an oval billiard we derive a trace formula for the ellipse which involves a uniform approximation for the maslov phases near the separatrix and a uniform approximation for tori of periodic orbits close to a bifurcation we then examine how the trace formula is modified when the ellipse is deformed into an oval this involves uniform approximations for the break up of tori and uniform approximations for bifurcations of periodic orbits relations between different uniform approximations are discussed

fixed point results for mappings satisfying ψ φ weakly contractive condition in partially ordered metric spaces abstract we establish coincidence fixed point and common fixed point theorems for mappings satisfying weakly contractive condition in an ordered complete metric space some applications of our obtained results are given

on iterations methods for zeros of accretive operators in banach spaces in this paper three iterations are designed to approach zeros of set valued accretive operators in banach spaces the first one is the continuous picard type iteration involving the resolvent the second one is the approximate picard type iteration involving the resolvent and the third one is the halpern type iteration involving the resolvent some strong convergence theorems for three iterations are proved

fixed point theorems for weakly contractive mappings in partially ordered sets abstract the purpose of this paper is to present some fixed point theorems for weakly contractive maps in a complete metric space endowed with a partial order

convergence of composite iterative methods for finding zeros of accretive operators abstract strong convergence theorems on composite iterative schemes by the viscosity approximation methods for finding a zero of an accretive operator are established in banach spaces the main results generalize the recent corresponding results of aoyama et al k aoyama y kimura w takahashi m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in banach spaces nonlinear anal 67 2007 2350 2360 ceng et al l c ceng a r khan q h ansari j c yao strong convergence of composite iterative schemes for zeros of m accretive operators in banach spaces nonlinear anal 70 2009 1830 1840 kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 and xu h k xu strong convergence of an iterative method for nonexpansive and accretive operators j math anal appl 314 2006 631 643 to viscosity methods in a strictly convex and reflexive banach space having a uniformly g teaux differentiable norm our results also improve the corresponding results of t d benavides g l acedo h k xu iterative solutions for zeros of accretive operators math nachr 248 249 2003 62 71 r chen z zhu viscosity approximation fixed points for nonexpansive and m accretive operators fixed point theory appl 2006 2006 1 10 s kamimura w takahashi approximation solutions of maximal monotone operators in hilbert spaces j approx theory 106 2000 226 240 p e mainge viscosity methods for zeroes of accretive operators j approx theory 140 2 2006 127 140 k nakajo strong convergence to zeros of accretive operators in banach spaces j nonlinear convex anal 7 2006 71 81

coincidence point theorems on metric spaces via simulation functions due to its possible applications fixed point theory has become one of the most useful branches of nonlinear analysis in a very recent paper khojasteh et al introduced the notion of simulation function in order to express different contractivity conditions in a unified way and they obtained some fixed point results in this paper we slightly modify their notion of simulation function and we investigate the existence and uniqueness of coincidence points of two nonlinear operators using this kind of control functions

fixed point theorems for non self mappings in symmetric spaces under φ weak contractive conditions and an application to functional equations in dynamic programming in this paper we prove some common fixed point theorems for two pairs of non self weakly compatible mappings enjoying common limit range property besides satisfying a generalized f weak contractive condition in symmetric spaces we furnish some illustrative examples to highlight the realized improvements in our results over the corresponding relevant results of the existing literature we extend our main result to four finite families of mappings in symmetric spaces using the notion of pairwise commuting mappings finally we utilize our results to discuss the existence and uniqueness of solutions of certain system of functional equations arising in dynamic programming

whispering gallery modes and resonances of an elliptic cavity eigenfunctions of the whispering gallery type in elliptic cavities are considered asymptotic expansions for resonances are derived from the uniform asymptotic expansions of mathieu functions and modified mathieu functions constructed by applying the langer olver method these asymptotic expansions are improved by including exponentially small terms which lie beyond all orders of the perturbative series and can be captured by carefully taking into account stokes s phenomenon a classification of resonances along the four irreducible representations of 2v the symmetry group of the elliptic cavity is provided and the splitting up of resonances is then understood in connection with the breaking of o 2 symmetry invariance under any rotation

fixed points of multivalued operators in ordered metric spaces with applications abstract the purpose of this paper is to present some new hybrid fixed point theorems involving multivalued operators which satisfy weakly generalized contractive conditions in an ordered complete metric space an example of the existence of solutions for a perturbed impulsive hyperbolic differential inclusion with variable times is given to illustrate the usability of our results

fixed points for φ ψ p weakly contractive mappings in metric spaces with w distance the fixed point theorems presented in this paper generalize recent results of dutta and choudhury 3 branciari 2 banach 1 rhoades 9 khan et al 6 kada 5 and rhoades and abbas 10

on ψ φ weakly contractive condition in partially ordered metric spaces recently heman kumar nashine and bessem samet h k nashine b samet fixed point results for mappings satisfying j f weakly contractive condition in partially ordered metric spaces nonlinear anal 74 2011 2201 2209 studied some coincidence fixed point and common fixed point theorems for two mappings satisfying j f weakly contractive condition in an ordered complete metric space in the present paper we study some coincidence fixed point and common fixed point theorems for three mappings s t and r satisfying j f weakly contractive condition in an ordered complete metric space where the mappings s and t are assumed to be weakly increasing with respect to r our results generalize several well known results in the literature

semiclassical study of particle motion in two dimensional and three dimensional elliptical boxes ii the authors compare three problems of quantum mechanics or more generally of wave mechanics which reduce to the same problem in classical mechanics and which can also be treated semiclassically by the einstein brillouin and keller 1958 semiquantisation rules the free particle motion in an ellipsoidal oblate or prolate cavity a deformed nucleus is compared to that in a plane elliptical billiard box separation of variables is performed in appropriate coordinate systems the presence of a separatrix in phase space is exhibited which is connected to a potential barrier that is different for each problem the uniform approximation is used to calculate wkb phase rules appropriate to each symmetry an important difference results between the prolate and the oblate systems

coincidence and common fixed point results in partially ordered cone metric spaces and applications to integral equations abstract in this paper coincidence and common fixed point results are established in a partially ordered cone metric space an application of our results obtained to prove the existence of a common solution to integral equations is presented

equivalent theorems of the convergence between proximal type algorithms abstract the main aim of this work is to give the equivalence of the convergence between proximal type algorithms our convergence analysis covers rockafellar type proximal point algorithm with a weak contraction for finding zeros of accretive operators as well as browder and halpern type iterations and viscosity approximation methods for finding fixed points of nonexpansive type mappings in banach spaces we also provide simple proofs of some results of wong sahu and yao n c wong d r sahu j c yao solving variational inequalities involving nonexpansive type mappings nonlinear anal 69 12 2008 4732 4753

exponentially improved asymptotic expansions for resonances of an elliptic cylinder scattering by an elliptic cylinder is considered asymptotic expansions for regge poles and resonances are derived from the uniform asymptotic expansions of mathieu functions and modified mathieu functions constructed by applying the langer olver method in addition asymptotic expansions for resonances are exponentially improved by emphasizing the role of the symmetries of the scatterer the splitting up of resonances is then explained in terms of the symmetry breaking o 2 2v

some coincidence point results in ordered b metric spaces and applications in a system of integral equations the aim of this paper is to present some coincidence point results for four mappings satisfying generalized j f weakly contractive condition in the framework of ordered b metric spaces an example and an application are also provided to support our results

existence and data dependence of fixed points for multivalued operators on gauge spaces abstract the purpose of this note is to present some fixed point and data dependence theorems in complete gauge spaces and in hyperconvex metric spaces for the so called meir keeler multivalued operators and admissible multivalued a contractions our results extend and generalize several theorems of espinola and kirk r espinola w a kirk set valued contractions and fixed points nonlinear anal 54 2003 485 494 and rus petrusel and sint m rian i a rus a petrusel a sint m rian data dependence of the fixed point set of some multivalued weakly picard operators nonlinear anal 52 2003 1947 1959

strong convergence of iterative methods by strictly pseudocontractive mappings in banach spaces abstract in this paper we deal with fixed point computational problems by strongly convergent methods involving strictly pseudocontractive mappings in smooth banach spaces first we prove that the s iteration process recently introduced by sahu in 14 converges strongly to a unique fixed point of a mapping t where t is strongly pseudocontractive mapping from a nonempty closed and convex subset c of a smooth banach space into itself it is also shown that the hybrid steepest descent method converges strongly to a unique solution of a variational inequality problem with respect to a finite family of i strictly pseudocontractive mappings from c into itself our results extend and improve some very recent theorems in fixed point theory and variational inequality problems particularly the results presented here extend some theorems of reich 1980 1 and yamada 2001 15 to a general class of strictly pseudocontractive mappings in uniformly smooth banach spaces

level crossings and commuting observables for the quantum elliptic billiard the energy spectrum of the quantum elliptic billiard is obtained by solving the schrodinger equation in elliptic coordinates the corresponding eigenstates also diagonalise an operator b which commutes with h a numerical search of the exact eigenvalues of b and h permits one to follow each state as a function of the deformation parameter mu geometrical arguments also valid for the simpler problem of the rectangular box allow one to understand the results obtained

some generalizations of caristi s fixed point theorem with applications to the fixed point theory of weakly contractive set valued maps and the minimization problem abstract in this paper we first prove some generalizations of caristi s fixed point theorem then we give some applications to the fixed point theory of weakly contractive set valued maps and the minimization problem

nonoscillatory solution of the steady state inviscid burgers equation by mathematical programming abstract numerical solution of the steady state inviscid burgers equation u2 0 on 0 1 u 0 g0 u 1 g1 g0 g1 is considered to obtain the physically relevant discontinuous solution of this problem the equation is singularly perturbed by adding a small amount of viscosity u u2 0 a cell entered finite difference scheme that uses two points for the inviscid part and four points for the viscous part is proposed the overdetermined nonlinear system that results is solved by a homotopy based on the newton linearizer and a linear programming algorithm used to solve l problems difficulties in capturing interior layers centered at node points are observed however the computational results for interior layers centered between node points and for boundary layers show accurate nonoscillatory solutions with discontinuities captured in one cell on both coarse and fine grids the amount of artificial viscosity required to obtain these solutions is small 10 9 compared to the amount of artificial viscosity required by standard methods a partial proof of pointwise and l1 0 1 convergence of the linear spline interpolant of the numerical solution to the inviscid solution h 0 and h 0 is given for one case

viscosity approximation methods with weak contraction for l lipschitzian pseudocontractive self mapping abstract in this paper under the framework of real reflexive banach space which admits a weakly sequentially continuous duality mapping from e to e we study the strong convergence of an implicit and an explicit composite viscosity approximation algorithm i and ii respectively for a pseudocontractive mapping t by using the weakly contractive mapping f as follows i x t s t f x t s 1 t y t s y t s s x t s 1 s t x t s and ii x n 1 n f x n 1 n y n y n n x n 1 n t x n n 0 our results unify improve and complement several recent ones existing in the current literature

some fixed point theorems using weaker meir keeler function in metric spaces with w distance abstract in the present paper we prove some new fixed point theorems for self mappings defined on a complete metric space with a w distance these results extend some previous fixed point theorems in this field to more general contractive conditions in the setting of w distances for selfmappings which satisfy certain weaker meir keeler conditions

equivalent conditions for generalized contractions on ordered metric spaces abstract we establish a geometric lemma giving a list of equivalent conditions for some subsets of the plane as its application we get that various contractive conditions using the so called altering distance functions coincide with classical ones we consider several classes of mappings both on metric spaces and ordered metric spaces in particular we show that unexpectedly some very recent fixed point theorems for generalized contractions on ordered metric spaces obtained by harjani and sadarangani j harjani k sadarangani generalized contractions in partially ordered metric spaces and applications to ordinary differential equations nonlinear anal 72 2010 1188 1197 and amini harandi and emami a amini harandi h emami a fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations nonlinear anal 72 2010 2238 2242 do follow from an earlier result of o regan and petrusel d o regan and a petrusel fixed point theorems for generalized contractions in ordered metric spaces j math anal appl 341 2008 1241 1252

boundary approximations for implicit schemes for one dimensional inviscid equations of gasdynamics the applicability to practical calculations of recent theoretical developments in the stability analysis of difference approximations is examined for initial boundary value problems of the hyperbolic type for the numerical experiments the one dimensional inviscid gasdynamic equations in conservation law form are selected a class of implicit schemes based on linear multistep methods for ordinary differential equations is chosen and the use of space or space time extrapolations as implicit or explicit boundary schemes is emphasized some numerical examples with various inflow outflow conditions highlight the commonly discussed issues explicit vs implicit boundary schemes and unconditionally stable schemes hen finite difference schemes are used to solve initial boundary value problems for the equations of fluid dynamics it is well known that most methods require more boundary conditions than those required by the governing partial differential equations these additional boundary conditions for the finite difference equations are often called numerical boundary conditions the numerical boundary conditions cannot be imposed arbitrarily but are determined in general using interior information for example by extrapolation or uncentered approximations in this paper any numerical procedure used to provide a numerical boundary condition will be called a boundary scheme whatever schemes are used for the numerical boundary conditions it is a common practice to assume that the boundary scheme has a local effect and will not affect the solution globally during the early 1970s kreiss 1 2 osher 3 gustafsson et al 4 varah 5 and gustafsson6 published a series of papers establishing methods for checking the stability and accuracy of difference approximations with boundary schemes included since then further progress has been made in the theory of linear difference approximations for initial boundary value problems of the hyperbolic and parabolic type 7 12 because improper treatment of the boundary conditions can lead to instability and inaccuracy even though we start with a stable interior scheme i e scheme for the interior points it is appropriate to adopt an approach that includes the stability and accuracy of the combined interior and boundary schemes surveys of recent developments and extensive bibliographies are included in papers by coughran13 and yee 14 the purpose of this paper is to examine the applicability to practical calculations for nonlinear gasdynamic problems of recent theoretical stability analyses of implicit difference approximations for initial boundary value problems of the hyperbolic type as numerical computations have progressed the use of the conservative form of the gasdynamic equations has gained popularity for physical reasons it is sometimes desirable to specify boundary conditions in the nonconservative variables and to compute with conservative variables in the interior we will consider the additional complications introduced by this procedure

cyclic generalized ψ weakly contractive mappings and fixed point results with applications to integral equations abstract we introduce a cyclic generalized weakly contractive mappings for a map in a metric space and originate existence and uniqueness results of fixed points for such mappings examples are given to support the usability of our results at the end of the results an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented

iterative approximation for a zero of accretive operator and fixed points problems in banach space abstract in this paper we introduced an iteration scheme for viscosity approximation for a zero of accretive operator and fixed points problems in a reflexive banach space with weakly continuous duality mapping a new iterative sequence is introduced and strong convergence of the algorithm xn is proved the results improve and extend the results of hu and liu l hu and l liu a new iterative algorithm for common solutions of a finite family of accretive operators nonlinear anal 70 2009 2344 2351 and some others

generalized contractions in partially ordered metric spaces and applications to ordinary differential equations the purpose of this paper is to present some fixed point theorems in a complete metric space endowed with a partial order by using altering distance functions we also present some applications to first and second order ordinary differential equations

a best proximity point theorem for weakly contractive non self mappings abstract let us consider a map t a b where a and b are two nonempty subsets of a metric space x the aim of this article is to provide sufficient conditions for the existence of a unique point x in a called the best proximity point which satisfies d x t x dist a b inf d a b a a b b our result generalizes a result due to rhoades b e rhoades some theorems on weakly contractive maps nonlinear analysis tma 47 2001 2683 2693 and hence it provides an extension of banach s contraction principle to the case of non self mappings

euler equations implicit schemes and boundary conditions implicit boundary condition procedures are presented for use with implicit finite difference schemes for the unsteady euler equations this new boundary point treatment is based on the mathematical theory of characteristics for hyperbolic systems of equations along with the theoretical background the practical application of the method to several types of boundaries is also explained using several examples the specific boundary conditions covered include subsonic inflow and outflow surface tangency and shock waves the example problems include one dimensional laval nozzle flow dual throat rocket engine nozzle flow and supersonic flow past a sphere the implicit boundary treatment permits the use of large time steps allowing the finite difference algorithm to converge to the asymptotic steady state much faster than schemes that use explicitly applied boundary conditions at least an order of magnitude increase in computational speed is demonstrated in the examples shown background t he growing popularity of solutions to the euler equations in transonics and their continued application in supersonics have increased the need for quicker solutions the potential of implicit schemes in this direction has not been fully exploited for want of correct implicit application of boundary conditions the predominant use of implicit algorithms for the navier stokes equations has partly been responsible for the neglect of implicit boundary point treatment for the euler equations thus there is a need for correct and stable procedures for the easy implicit application of boundary conditions such methods will serve the two purposes of 1 reaching time asymptotic steady state faster and 2 permitting a time step for truly unsteady flow that is not necessarily restricted by the cfl stability criterion but is based upon the magnitude of the transients for clues and information on how to construct such boundary condition procedures one must turn to the mathematical theory of characteristi cs for hyperbolic systems of equations the unsteady euler equations belong to this category the theory for hyperbolic systems is rich with information on signal propagation directions the characteristics theory clearly points to the number of boundary conditions that may and need be prescribed without overdetermining the solution boundary condition procedures based on this theory have been known and applied for several years by kentzer 1 porter and coakley 2 de neef 3 and others in earlier work by this author 4 5 easily understood and implementable methods for boundary point treatment were presented however all of the above techniques were developed for explicit finite difference schemes it seems that it must be easy to extend such methodologies based on mathematical theory for hyperbolic systems to implicit finite difference schemes and indeed it is simple enough the rest of this paper describes such implicit boundary condition procedures the given examples illustrate in detail the application of the proposed methodology to specific types of boundaries and demonstrate the merits of the new scheme

existence and approximation of fixed points of nonlinear mappings in spaces with weak uniform normal structure it is shown that in a banach space x with weak uniform normal structure every demicontinuous asymptotically regular nearly lipschitzian self mapping t with lim sup n h t n

generalized coupled fixed points and its application to a class of systems of functional equations arising in dynamic programming in this paper we introduce the definition of generalized coupled fixed point in the space of the bounded functions on a set s and we prove a result about the existence and uniqueness of such points as an application of our result we study the problem of existence and uniqueness of solutions for a class of systems of functional equations which appears in dynamic programming

dynamical diffraction in sinusoidal potentials uniform approximations for mathieu functions eigenvalues and fourier space eigenfunctions of mathieu s equation are found in the short wavelength limit using a uniform approximation method of comparison with a known equation having the same classical turning point structure applied to the raman nath rn equation the uniform approximation used here relies upon the fact that by passing into fourier space the mathieu equation can be mapped onto the simpler problem of a double well potential the resulting eigenfunctions bloch waves which are uniformly valid for all angles are then used to describe the semiclassical scattering of waves by potentials varying sinusoidally in one direction in such situations for instance in the diffraction of atoms by gratings made of light it is common to make the rn approximation which ignores the motion of the atoms inside the grating when using the eigenfunctions no such approximation is made so that the dynamical diffraction regime long interaction time can be explored

the point of coincidence and common fixed point for a pair of mappings in cone metric spaces in this paper the existence of a point of coincidence and a common fixed point for two weakly compatible maps on a cone metric space has been established the two mappings are assumed to satisfy certain weak inequalities supporting examples are also given

fixed point theory for cyclic φ contractions abstract following w a kirk p s srinivasan p veeramany fixed points for mappings satisfying cyclical contractive conditions fixed point theory 4 1 2003 79 89 we present a fixed point theorem for cyclic contractions and following i a rus the theory of a metrical fixed point theorem theoretical and applicative relevances fixed point theory 9 2 2008 541 559 we construct a theory of this fixed point theorem this theory is in connection with data dependence well posedness of the fixed point problem limit shadowing property and sequences of operators and fixed points a maia type fixed point theorem for cyclic contractions is also given

calculation of shocked one dimensional flows on abruptly changing grids by mathematical programming abstract the steady state inviscid and nearly inviscid burgers equations and the euler equations for steady state shocked flow in a quasi 1 dimensional nozzle are discretized by cell centered finite differences on the cells of an arbitrarily spaced grid inviscid and viscous terms are approximated to second order by 2 point schemes and 4 point schemes respectively there results an overdetermined system of nonlinear algebraic equations this system is solved by a mathematical programming procedure that minimizes a weighted sum of the absolute values of the residuals the l 1 norm of the vector of residuals in this algorithm which is nonconservative no upwinding switches arbitrary constants or heuristic quantities are used the artificial viscosity used to solve the inviscid burgers equation is small 10 15 u no artificial viscosity of any kind is used for the euler equations the numerical solutions of both the viscous and the inviscid problems are accurate and nonoscillatory on grids with abrupt refinements in mesh length by factors as high as 10 4 shocks are invariably captured in one cell and this cell is rarely more than three cells away from the cell in which the physical shock occurs