fixed points of weakly inward multivalued maps on considere le probleme suivant etant donnes un espace de banach reel x un convexe borne clos k x et f k 2 x o satisfaisant f est semi continue superieurement f x est convexe clos x k f est condensante et f x k x o x k f a t elle un point fixe

approximation and fixed point theorems for condensing composites of multifunctions one of the authors previously extended an interesting best approximation theorey of ky fan to condensing maps defined on a closed ball in a banach space and defined on a closed convex subset in a hilbert space recently there have appeared a number of new results on fixed points of so called kakutani factorizable multifunctions or composites of acyclic or other type of multifunctions defined on convex subsets of topological vector spaces in this paper we extend lin s results to the multifunction or set valued version for the above mentioned factorizable multifunctions applications to fixed point theorems are given

fixed point and approximation results for multimaps in s kkm class the paper discusses new fixed point and approximation theorems for multimaps in the class s kkm

on the meaning of randomness in stochastic environmental models this paper describes and explains the differences between two different approaches toward stochastic water quality modeling two groups of models namely models based on differential equations with coefficients being either random variables random variable models or stochastic processes stochastic process models are analyzed the reasoning behind these two approaches is discussed and a numerical example illustrating the possible consequences in estimating stochastic characteristics of the solution process using either of these two approaches is presented and discussed

method of lines solution of the korteweg de vries equation abstract the korteweg de vries equation kdve is a classical nonlinear partial differential equation pde originally formulated to model shallow water flow in addition to the applications in hydrodynamics the kdve has been studied to elucidate interesting mathematical properties in particular the kdve balances front sharpening and dispersion to produce solitons i e traveling waves that do not change shape or speed in this paper we compute a solution of the kdve by the method of lines mol and compare this numerical solution with the analytical solution of the kdve in a second numerical solution we demonstrate how solitons of the kdve traveling at different velocities can merge and emerge the numerical procedure described in the paper demonstrates the ease with which the mol can be applied to the solution of pdes using established numerical approximations implemented in library routines

analysis of transient flow in pipelines with fluid structure interaction using method of lines a mathematical model is presented for transient flow in a pipeline with fluid structure interaction water hammer theory and equations of axial motion for the pipeline are employed and the poisson junction and transient shear stress couplings are taken into account which give rise to four coupled non linear first order hyperbolic partial differential equations governing the fluid flow and pipe motion these equations are discretized in space using the keller box scheme and the method of lines is employed to reduce the partial differential equations to a system of ordinary differential equations the resulting system is solved using a backward differentiation formulation method the effect of transient shear stress on transient flow is investigated and the mechanisms underlying this effect are explored the results revealed that the influence of transient shear stress can be significant and varies considerably depending on the boundary conditions viz valve closure time copyright 2005 john wiley sons ltd

comparison of first order error analysis and monte carlo simulation in time dependent lake eutrophication models estimates of variance for a nonlinear seasonal food chain nutrient cycle eutrophication model of saginaw bay lake huron calculated by first order variance propagation and monte carlo analyses do not always agree a comparison of estimates of state variables indicates that monte carlo means are most like the measurements whereas monte carlo medians are most like the deterministic model output best agreement between monte carlo and first order estimates of both state variable values and their variances occurs when monte carlo output distributions are symmetric under these conditions both estimates are measures of variance associated with total populations i e all algae those distributions however change dramatically in time for most state variables for asymmetric distributions first order variance estimates measure variability about the typical component of the total population i e the typical algal species and monte carlo variance estimates measure variability of the mean component which is more reflective of the total one must be cognizant of these differences when estimating variance associated with model projections

nonlocal reactive transport with physical and chemical heterogeneity localization errors the origin of nonlocality in macroscale models for subsurface chemical transport is illustrated it is argued that media that are either nonperiodic e g media with evolving heterogeneity or periodic viewed on a scale wherein a unit cell is discernible must display some nonlocality in the mean a metaphysical argument suggests that owing to the scarcity of information on natural scales of heterogeneity and on scales of observation associated with an instrument window constitutive theories for the mean concentration should at the outset of any modeling effort always be considered nonlocal the intuitive appeal to nonlocality is reinforced with an analytical derivation of the constitutive theory for a conservative tracer without appeal to any mathematical approximations deng et al 1993 present a first order nonlocal eulerian theory for transport of a conservative solute in an infinite nondeforming domain under steady flow conditions hu et al this issue extended these results to account for nonequilibrium linear sorption with random partition coefficient kd but deterministic constant reaction rate kr these theories are localized herein and comparisons are made between the fully nonlocal fnl nonlocal in time nlt and fully localized fl theories for conservative transport there is little difference between the first order fl and fnl models for spatial moments up to and including the third however for conservative transport the first order nlt model differs significantly from the fnl model in the third spatial moments for reactive transport all spatial moments differ between the fnl and fl models the second transverse horizontal and third longitudinal horizontal moments for the nlt model differ from the fnl model these results suggest that localized first order transport models for conservative tracers are reasonable if only lower order moments are desired however when the chemical reacts with its environment the localization approximation can lead to significant error in all moments and a fnl model will in general be required for accurate simulation

direct numerical methods for solving a class of third order partial differential equations in this paper three types of third order partial differential equations pdes are classified to be third order pde of type i ii and iii these classes of third order pdes usually occur in many subfields of physics and engineering for example pde of type i occurs in the impulsive motion of a flat plate an efficient numerical method is proposed for pde of type i the pde of type i is converted to a system of third order ordinary differential equations odes using the method of lines the system of odes is then solved using direct runge kutta which we derived purposely for solving special third order odes of the form y f x y simulation results showed that the proposed rkd based method is more accurate than the existing finite difference method

fixed point theorems for compact multimaps on almost γ convex sets in generalized convex spaces abstract in this paper we introduce the concept of the strict kakutani multimap kkm property and investigate the fixed point problem for multimaps having this property on almost convex subsets of locally g convex uniform spaces our new fixed point theorem generalizes the well known fan glicksberg fixed point theorem and partially extends the himmelberg fixed point theorem its application to minimax theorem is also given

a super accurate shifted tau method for numerical computation of the sobolev type differential equation with nonlocal boundary conditions in this article we propose a super accurate numerical scheme to solve the one dimensional sobolev type partial differential equation with an initial and two nonlocal integral boundary conditions our proposed methods are based on the shifted standard and shifted chebyshev tau method firstly we convert the model of partial differential equation to a linear algebraic equation and then we solve this system shifted standard and shifted chebyshev polynomials are applied for giving the computational results numerical results are presented for some problems to demonstrate the usefulness and accuracy of this approach the method is easy to apply and produces very accurate numerical results

stiffness characteristic and the applications of the method of lines on nonuniform grids the method of lines is investigated for the numerical solution of the stream function and vorticity form of the navier stokes equations on nonuniform grids stiffness characteristics of a linear one dimensional model equation are examined to establish the feasibility of applying the method to the vorticity equation in two dimensions the governing equations are transformed from the physical domain with a highly variable grid to a computational domain with a uniform grid the method of lines is used to solve only the vorticity equation and the successive over relaxation technique is used to solve the stream function equation it is observed that the transformed governing equations become stiffer with increased concentration of grid points and also as the number of grid points increases it is also observed that the differencing technique affects the stiffness characteristics the use of forward differencing is not feasible and backward differencing is preferable to central differencing for high reynolds numbers the results of specific applications for the solution of flow in curved wall diffusers and a driven cavity demonstrate that the method of lines under certain circumstances is feasible for the numerical solution of physical problems on domains covered with variable grids

the solution of the boussinesq equation using the method of lines abstract the method of lines is used to transform the initial boundary value problem associated with the nonlinear hyperbolic boussinesq equation into a first order nonlinear initial value problem numerical methods are developed by replacing the matrix exponential term in a recurrence relation by rational approximants the resulting finite difference methods are analysed for local truncation errors stability and convergence the results of a number of numerical experiments are given

numerical treatment of stochastic river quality models driven by colored noise 1 monte carlo simulation is a popular method of risk and uncertainty analysis in oceanographic atmospheric and environmental applications it is common practice to introduce a stochastic part to an already existing deterministic model and after many simulations to provide the user with statistics of the model outcome the underlying deterministic model is often a discretization of a set of partial differential equations describing physical processes such as transport turbulence buoyancy effects and continuity much effort is also put into deriving numerically efficient schemes for the time integration the resulting model is often quite large and complex in sharp contrast the stochastic extension used for monte carlo experiments is usually achieved by adding white noise unfortunately the order of time integration in the stochastic model is reduced compared to the deterministic model because white noise is not a smooth process instead of completely replacing the old numerical scheme and implementing a higher order scheme for stochastic differential equations we suggest a different approach that is able to use existing numerical schemes the method uses a smooth colored noise process as the driving force resulting in a higher order of convergence we show promising results from numerical experiments including parametric uncertainty

exact solutions and conservation laws for coupled generalized korteweg de vries and quintic regularized long wave equations abstract a new model equation is proposed for simulating unidirectional wave propagation in nonlinear media with dispersion this model equation is a one dimensional evolutionary partial differential equation that is obtained by coupling the generalized korteweg de vries gkdv equation which includes a nonlinear term of any order and cubic dispersion with the quintic regularized long wave qrlw equation which includes fifth order dispersion exact solitary wave solutions are derived for this model equation these analytical solutions are obtained for any order of the nonlinear term and for any given values of the coefficients of the cubic and quintic dispersive terms analytical expressions for three conservation laws and for three invariants of motion for solitary wave solutions of this new equation are also derived

fixed point theorems for multifunctions having kkm property on almost convex sets in this paper for two nonempty subsets x and y of a linear space e we define the class kkm x y and investigate the fixed point problem for t kkm x x with x an almost convex subset of a locally convex space our fixed point theorem contains lassonde fixed point theorem for kakutani factorizable multifunctions as special case

on general best proximity pairs and equilibrium pairs in free abstract economies abstract in this paper using lassonde s fixed point theorem for kakutani factorizable multifunctions and park s fixed point theorem for acyclic factorizable multifunctions we will prove new existence theorems for general best proximity pairs and equilibrium pairs for free abstract economies which generalize the previous best proximity theorems and equilibrium existence theorems due to srinivasan and veeramani p s srinivasan p veeramani on best approximation pair theorems and fixed point theorems abstr appl anal 2003 1 2003 33 47 p s srinivasan p veeramani on existence of equilibrium pair for constrained generalized games fixed point theory appl 2004 1 2004 21 29 and kim and lee w k kim k h lee existence of best proximity pairs and equilibrium pairs j math anal appl 316 2006 433 446 in several aspects

efficient time integrators in the numerical method of lines the numerical method of lines has long been acknowledged as a very powerful approach to the numerical solution of time dependent partial differential equations this method in its original form involved making a simple approximation to the space derivatives and by so doing reducing the problem to that of solving a system of initial value ordinary differential equations and then using a black box package as the time integrator however in the past twenty years or so moving mesh algorithms in space have been developed and this allows much more challenging problems for example those with moving fronts to be solved efficiently and reliably regridding of the space variables poses special problems for the time integrator since sufficient back information to allow multistep formulae to run at high order is not available immediately after the regridding has been performed in this paper we survey some of the options available for the time integration when using a moving grid method of lines code in particular we derive runge kutta starters for use after grid adaptation has been carried out and we show how a considerable saving in computational effort can be made if just a few spatial points are moved during each regridding

application of the ritz galerkin method for recovering the spacewise coefficients in the wave equation an inverse problem for the determination of the unknown spacewise dependent coefficients in a hyperbolic equation through additional boundary measurements is considered for the sake of simplicity the problem has been considered in one dimension however the method is applicable for problems with regular and bounded domains in higher dimensions the technique provides space time approximations for the wave equation by expanding the required approximate solutions using the bernstein multi scaling functions the key feature of the approach is applying the ritz galerkin method along with utilizing the satisfier function which fulfills all the initial and boundary conditions as well as the consequences only a low number of basis is required to find satisfactory results which lead to reliably less computations in comparison to other published methods despite the assumptions of sufficiently smooth initial and boundary conditions to guarantee a unique solution this solution is unstable this fact is confirmed by the numerical findings that show the errors in the approximations are relatively large i e they are not of the same order compared to the noise levels greater than 3 hence the problem is ill posed to alleviate the difficulties arising from solving the ill posed problems a type of particular regularization technique which consists in repeatedly linearizing the operator equation f x y is utilized numerical results are presented for the typical benchmark test examples which have the input measured data perturbed by increasing amounts of noise the numerical investigations are included showing that accurate and stable results can be obtained efficiently with small computational cost

existence of best proximity pairs and equilibrium pairs in this paper using the fixed point theorem for kakutani factorizable multifunctions we shall prove new existence theorems of best proximity pairs and equilibrium pairs for free abstract economies which include the previous fixed point theorems and equilibrium existence theorems

comparison of method of lines and finite difference solutions of 2 d navier stokes equations for transient laminar pipe flow performances of method of lines mol and finite difference method fdm were tested from the viewpoints of solution accuracy and central processing unit cpu time by applying them to the solution of time dependent 2 d navier stokes equations for transient laminar flow without with sudden expansion and comparing their results with steady state numerical predictions and measurements previously reported in the literature predictions of both methods were obtained on the same computer by using the same order of spatial discretization and the same uniform grid distribution axial velocity and pressure distribution in pipe flow and steady state reattachment lengths in sudden expansion flow on uniform grid distribution predicted by both methods were found to be in excellent agreement transient solutions of both methods for pipe flow problem show favourable comparison and are in accordance with expected trends however non physical oscillations were produced by both methods in the transient solution of sudden expansion pipe flow mol was demonstrated to yield non oscillatory solutions for recirculating flows when intelligent higher order discretization scheme is utilized for convective terms mol was found to be superior to fdm with respect to cpu and set up times and its flexibility for incorporation of other conservation equations

a theorem on the minimization of a condensing multifunction and fixed points abstract let g be a subset of a locally convex separated topological vector space e with int g o cl g convex and quasi complete let f cl g e be a continuous condensing multifunction with compact and convex values and with a bounded range it is shown that for each w int g there exists a u u w cl g such that p f u u inf p x y x f u y cl g where p is the minkowski s functional of the set cl g w several fixed point results are obtained as a consequence of this result

fixed points for kakutani factorizable multifunctions abstract a multifunction is called a kakutani multifunction if there exist two nonempty convex sets x and y each in a hausdorff topological vector space such that x y is upper semi continuous with nonempty compact convex values we prove the following extension of the kakutani fixed point theorem let x x be a multifunction from a simplex x into itself if can be factorized by an arbitrary finite number of kakutani multifunctions then has a fixed point the proof relies on a simplicial approximation technique and the brouwer fixed point theorem extensions to infinite dimensional spaces and applications to game theory are given

the method of lines for the numerical solution of a mathematical model for capillary formation the role of endothelial cells in the capillary abstract in this paper we present the method of lines to obtain the numerical solution of a mathematical model for capillary formation in tumor angiogenesis this method is an approach to the numerical solution of partial differential equations that involve a time variable t and space variables x y as the number of lines is increased the accuracy of the method of lines representation of the original system increases the method provides very accurate numerical solutions for linear and nonlinear problems in comparison with other existing methods we also provide computer programs written in matlab and figures that show the endothelial cell movement

the operational matrices of bernstein polynomials for solving the parabolic equation subject to specification of the mass abstract some physical problems in science and engineering are modelled by the parabolic partial differential equations with nonlocal boundary specifications in this paper a numerical method which employs the bernstein polynomials basis is implemented to give the approximate solution of a parabolic partial differential equation with boundary integral conditions the properties of bernstein polynomials and the operational matrices for integration differentiation and the product are introduced and are utilized to reduce the solution of the given parabolic partial differential equation to the solution of algebraic equations illustrative examples are included to demonstrate the validity and applicability of the new technique

compressibility a property of topological spaces related to abstract convexity abstract an abstract operation of hull in a set y associates with every finite set f y a set hull f y a topological space x is said to be compressible into a topological space y equipped with an operation of hull if for every sequence a1 an of open sets covering x and every y1 yn yn there exists a continuous function x y such that for every x x x hull y i x a i the concept of compressibility is extremely useful when dealing with problems of the existence of fixed points continuous selections or with kkm property the obtained results generalize several known theorems they also provide a broad range of new original results

best proximity pairs and equilibrium pairs for kakutani multimaps new existence theorems of best proximity pairs for a finite family of kakutani multimaps are proved in a normed space setting as applications new existence theorems of equilibrium pairs for free n person and 1 person games are obtained our results generalize and improve several well known results 2008 elsevier ltd all rights reserved

numerical integration of stochastic differential equations in catchment modeling the paper discusses appropriate integration procedures for deriving solutions to stochastic differential equations sde s such sde s have been suggested as models for the generation of stochastic streamflows from catchments the sde s have been developed by expanding the nash cascade to include random inputs of rainfall and catchment abstractions the numerical integration of the sde provides sample functions that can be considered as representations of streamflows examples are given

fixed points coincidence points and maximal elements with applications to generalized equilibrium problems and minimax theory abstract in this paper using a generalization of the fan browder fixed point theorem we obtain a new fixed point theorem for multivalued maps in generalized convex spaces from which we derive several coincidence theorems and existence theorems for maximal elements applications of these results to generalized equilibrium problems and minimax theory will be given in the last sections of the paper

an approximation technique for stochastic environmental modeling this paper describes the outline of an approximate mathematical technique capable of including stochastic components in environmental models based on ordinary differential equations the technique is based on the decomposition of the solution into additive components with the first component being the solution of a simplified deterministic equation and each of the other components being found in terms of those preceding it moments of the solution process can then be calculated by performing appropriate averaging the method provides natural statistical separability that is no truncations in the derivation stage or closure approximations are necessary the random quantities involved can be either random variables or stochastic processes no unrealistic assumptions like white noise behavior or small randomness are necessary solutions which are in the form of infinite but convergent series can be easily implemented into computer programs providing convenient support in management and decision analysis a demonstration application of a simple biochemical oxygen demand model for river waters illustrates the usefulness of the technique in environmental modeling

method of lines study of nonlinear dispersive waves in this study we consider partial differential equation problems describing nonlinear wave phenomena e g a fully nonlinear third order korteweg de vries kdv equation the fourth order boussinesq equation the fifth order kaup kupershmidt equation and an extended kdv5 equation first we develop a method of lines solution strategy using an adaptive mesh refinement algorithm based on the equidistribution principle and spatial regularization techniques on the resulting highly nonuniform spatial grids the computation of high order derivative terms appears particularly delicate and we focus attention on the selection of appropriate approximation techniques finally we solve several illustrative problems and compare our computational approach to conventional solution techniques

method of lines solutions of the extended boussinesq equations a numerical solution procedure based on the method of lines for solving the nwogu one dimensional extended boussinesq equations is presented the numerical scheme is accurate up to fifth order in time and fourth order accurate in space thus reducing all truncation errors to a level smaller than the dispersive terms retained by most extended boussinesq models exact solitary wave solutions and invariants of motions recently derived by the authors are used to specify initial data for the incident solitary waves in the numerical model of nwogu and for the verification of the associated computed solutions the invariants of motions and several error measures are monitored in order to assess the conservative properties and the accuracy of the numerical scheme the proposed method of lines solution procedure is general and can be easily modified to solve a wide range of boussinesq like equations in coastal engineering

a good spatial discretisation in the method of lines in this paper a method of lines is proposed for solving partial differential equations a suitable spatial discretisation is introduced then the numerical examples show that the method of lines is feasible and very effective for solving parabolic problems

the constrained degree and fixed point index theory for set valued maps abstract in the first part of the paper we give a construction of a topological degree theory for set valued tangent vector fields with convex and nonconvex values defined on nonsmooth closed subsets of a banach space the obtained homotopy invariant is an extension of the classical degree for vector fields on manifolds in the second part we propose a fixed point index for inward maps on arbitrary closed convex sets

the method of lines for the numerical solution of a mathematical model for capillary formation the role of tumor angiogenic factor in the extra cellular matrix abstract in this paper we present the method of lines for the numerical solution of a mathematical model for capillary formation in two space dimensions x y we study the tumor angiogenic factor taf equation and suppose there is no tumor source supplied to the system for simplicity this method is an approach to the numerical solution of partial differential equations that involve a time variable t and space variables x y we provide computer programs written in matlab for linear and nonlinear case and provide figures that show the taf progression in time

approximation theorems and fixed point theorems for multivalued condensing mappings in wedges abstract in this paper we first prove the following best approximation theorems let e be a hausdorff locally convex space and w be a wedge in e let d be an open subset of e with d such that the closure d of d is convex suppose that f d w ck w is a continuous condensing mapping then there exists e 0 d w such that d p d w f e 0 e 0 d p d w f e 0 d w where p d w denotes the minkowskii function of d w in e moreover if d p d w f e 0 d w 0 then e 0 d w as a direct consequence we improve and generalize the main results of fan lin and sehgal and singh next we show several best approximation theorems and fixed point theorems for multivalued k set contractive mapping defined on the closed balls and annulus in cones of banach spaces which generalize the recent results of lin and sehgal and singh

the method of lines for solution of the one dimensional wave equation subject to an integral conservation condition hyperbolic partial differential equations with an integral condition serve as models in many branches of physics and technology recently much attention has been expended in studying these equations and there has been a considerable mathematical interest in them in this work the solution of the one dimensional nonlocal hyperbolic equation is presented by the method of lines the method of lines mol is a general way of viewing a partial differential equation as a system of ordinary differential equations the partial derivatives with respect to the space variables are discretized to obtain a system of odes in the time variable and then a proper initial value software can be used to solve this ode system we propose two forms of mol for solving the described problem several numerical examples and also some comparisons with finite difference methods will be investigated to confirm the efficiency of this procedure

numerical method using cubic b spline for the heat and wave equation in the present paper the cubic b splines method is considered for solving one dimensional heat and wave equations a typical finite difference approach had been used to discretize the time derivative while the cubic b spline is applied as an interpolation function in the space dimension the accuracy of the method for both equations is discussed the efficiency of the method is illustrated by some test problems the numerical results are found to be in good agreement with the exact solution

random differential equations in river water quality modeling a one dimensional steady state probabilistic river water quality model is developed to compute the joint and marginal probability density functions of bod and do at any point in a river the model can simultaneously consider randomness in the initial conditions inputs and coefficients of the water quality equations any empirical or known distribution can be used for the initial conditions randomness in each of the water quality equation inputs and coefficients is modeled as a gaussian white noise process the joint probability density function pdf of bod and do is determined by numerically solving the fokker plank random differential equation in addition moment equations are developed which allow the mean and variance of bod and do to be calculated independently of their joint pdf the probabilistic river water quality model is examined through sensitivity study and an application to a hypothetical river system

a radial basis functions based finite differences method for wave equation with an integral condition the hyperbolic partial differential equation which contains integral condition in place of classical boundary condition arises in many application of modern physics and technologies in this article we propose a numerical method to solve the hyperbolic equation with nonlocal boundary condition using radial basis function based finite difference method several numerical experiments are presented and compared with some existing method to demonstrate the efficiency of the proposed method

the direct method of lines for the numerical solutions of interface problem abstract in this paper a direct method of lines is proposed for solving the interface problem on a polygonal domain numerically a suitable transformation of coordinates is introduced then the interface problem is reduced to a variational differential problem on a semi infinite strip in the new variables and furthermore the variational differentional problem is discretized respect with variable thus we obtain the semi discrete approximation of the interface problem finally the optimal error estimate of the semi discrete approximation is given and the numerical examples show that the direct method of lines is feasible and very effective for solving the interface problem numerically

coincidence and maximal element theorems and their applications to generalized equilibrium problems and minimax inequalities abstract in this paper we obtain first a very general coincidence theorem from this we derive a new coincidence theorem and two alternative theorems concerning existence of maximal elements applications of these results to generalized equilibrium problems and minimax inequalities are given in the last sections

a numerical solution to nonlinear second order three point boundary value problems in the reproducing kernel space abstract in this paper a new numerical algorithm is provided to solve nonlinear three point boundary value problems in a very favorable reproducing kernel space which satisfies all boundary conditions its reproducing kernel function is discussed in detail we also prove that the approximate solution and its first and second order derivatives all converge uniformly the numerical experiments show that the algorithm is quite accurate and efficient for solving nonlinear second order three point boundary value problems

the application of cubic trigonometric b spline to the numerical solution of the hyperbolic problems in this paper a collocation finite difference scheme based on new cubic trigonometric b spline is developed and analyzed for the numerical solution of a one dimensional hyperbolic equation wave equation with non local conservation condition the usual finite difference scheme is used to discretize the time derivative while a cubic trigonometric b spline is utilized as an interpolation function in the space dimension the scheme is shown to be unconditionally stable using the von neumann fourier method the accuracy of the proposed scheme is tested by using it for several test problems the numerical results are found to be in good agreement with known exact solutions and with existing schemes in literature

an analytic technique for stochastic analysis in environmental models this paper describes the development and application of a new mathematical technique to include stochasticity in environmental models the technique named the probability density function moment pdf m technique by the authors is based on a two tiered process first the basic governing equations are expanded to include stochastic terms stochastic terms are separated from nonfluctuating terms and the resulting set of equations is solved simultaneously solutions are used to calculate the moments of the output variables second the moments are used in conjunction with the fokker planck equation to produce an analytical solution for the probability density functions of the dependent variables because the approach produces analytical solutions it offers greater flexibility than a monte carlo approach in treating complex environmental situations unlike the stochastic differential equation approach it is not necessary to assume gaussian distributions in the solution technique complex random functions of time and space may be included and solutions are possible for higher dimensioned problems and cases with stochastic variations in stream velocity the pdf m technique represents a new and potentially powerful tool for extending the capabilities of computer models in management and decision analysis by providing analytical solutions for the probability density functions and associated moments of important environmental variables

method of lines approximations of delay differential equations we consider a special type of numerical methods for delay differential equations ddes by introducing a new independent variable an initial value problem for ddes is converted into an initial boundary value problem for the convection equation thus it is also possible to get an approximate solution to the dde problem by solving the initial boundary value problem with a suitable numerical method instead of solving the original problem in this paper we study a family of method of lines mol approximations to the problem which is obtained by applying runge kutta rk methods for space discretization and prove their convergence under the assumption that the rk methods satisfy a condition known as an algebraic characterization of a stability the result is also confirmed by numerical experiments moreover we show that the condition derives several stability properties of the mol approximations

adaptive method of lines solutions for the extended fifth order korteweg de vries equation in this paper we investigate the dynamics and interaction properties of recently discovered embedded solitons in an extended fifth order kdv model inspired by water waves in the presence of surface tension the dynamical behaviour of the solitons can be efficiently followed by using a moving or an adaptive finite difference mesh in combination with a suitable time integrator we will demonstrate this numerically for different types of wave solutions such as solitary waves multihumped waves and interacting waves

fixed points of weakly inward maps in conical shells soit x un espace de banach reel k x un cone et f kr x x x r x compacte ou condensante on recherche les points fixes de f dans une coque conique k r x k x r

the bolzano mean value theorem and partial differential equations abstract we study the existence of solutions to abstract equations of the form 0 a u f u u k e where a is an abstract differential operator acting in a banach space e k is a closed convex set of constraints being invariant with respect to resolvents of a and a perturbation f satisfies a certain tangency condition such problems are closely related to the so called poincare miranda theorem being the multi dimensional counterpart of the celebrated bolzano intermediate value theorem in fact our main results should be regarded as infinite dimensional variants of bolzano and miranda poincare theorems along with single valued problems we deal with set valued ones yielding the existence of the so called constrained equilibria of set valued maps the abstract results are applied to show existence of strong steady state solutions to some weakly coupled systems of drift reaction diffusion equations or differential inclusions of this type in particular we get the existence of strong solutions to the dirichlet neumann and periodic boundary problems for elliptic partial differential inclusions under the presence of state constraints of different type certain aspects of the bernstein theory for bvp for second order ode are studied too no assumptions concerning structural coupling monotonicity cooperativity are undertaken

fixed points of weakly inward multis soit x un espace de banach reel k x convexe ferme borne f k 2 x semicontinue superieurement et condensant f x convexe ferme x k et f faiblement interieur sur k alors f a un point fixe

homotopy invariants for tangent vector fields on closed sets abstract in the paper we construct a topological degree theory for single and convex valued tangent vector fields defined on locally compact closed subsets of a banach space the obtained homotopy invariant is an extension of the classical degree for vector fields on manifolds the degree allows to study vector fields on sets which are neither smooth nor convex and may be applied to study continuation and bifurcation of equilibria in parameterized families of closed sets

sharpened forms of coincidence theorems and variational inequalities for fuzzy mappings abstract the aim of this paper is to generalize and to sharpen recent results of chang 1994 on coincidence point and variational inequalities for fuzzy mappings our generalizations are summarized as follows to begin with we remove some essential conditions which chang s results cannot do without secondly we provide very simple proofs for those results of chang finally we extend chang s theorem on coincidence points between to spaces to the case of n 2 spaces in addition we use non compact settings all the above refinements can be simultaneously achieved with the aid of some known results due to kum 1994 and simons 1986

banach ultrapowers and multivalued nonexpansive mappings the banach ultrapower construction is applied in fixed point theory for multivalued mappings we introduce the notion of ultra asymptotic centers and use it to remove the separability assumption from the results of dominguez benavides lorenzo ramirez 2004 and dhompongsa kaewcharoen kaewkhao 2006

the solution of the two dimensional sine gordon equation using the method of lines the method of lines is used to transform the initial boundary value problem associated with the two dimensional sine gordon equation in two space variables into a second order initial value problem the finite difference methods are developed by replacing the matrix exponential term in a recurrence relation with rational approximants the resulting finite difference methods are analyzed for local truncation error stability and convergence to avoid solving the nonlinear system a predictor corrector scheme using the explicit method as predictor and the implicit as corrector is applied numerical solutions for cases involving the most known from the bibliography line and ring solitons are given

local variably scaled newton basis functions collocation method for solving burgers equation abstract in the present paper a meshless method which constructs derivatives discretizations based on variably scaled newton basis functions vsnbfs interpolants for localized sets of nodes is provided to solve burgers equation in the native hilbert space of the reproducing kernel using such formulas for discretizations of pdes when each internal node considered as a center leads to a sparse global of system of ordinary differential equations odes to be formed by a simple assembly of function values at the local system centrepoints for efficiency and stability reasons we use the interpolation with variably scaled kernels which are introduced recently by bozzini et al the vsnbfs can be constructed from a symmetric positive definite variably scaled kernel the main advantage of using the local method is that the overlapping domains of influence result in many small matrices with the dimension of the number of nodes included in the domain of influence for each center node instead of a large collocation matrix and hence sparse global derivative matrices from local contributions therefore the method needs less computer storage and flops the method is tested on six benchmark problems on burgers equation with mixed boundary conditions five number of nodes are used in the domain of influence of the local support the numerical results for different values of reynolds numbers re are compared with analytical solutions as well as some other numerical methods it is shown that the proposed method is efficient accurate and stable for flow with reasonably high values of re numerical results also show that using variably scaled kernels leads to results that are better than using constant scaled kernels with respect to both stability and error