positive solutions for the boundary value problems of one dimensional p laplacian with delay this paper is concerned with the existence of positive solutions for the boundary value problem of one dimensional p laplacian with delay the proof is based on the guo krasnoselskii fixed point theorem in cones

nontrivial solutions of m point boundary value problems for singular second order differential equations with a sign changing nonlinear term this paper concerns the existence of nontrivial solutions for the following singular m point boundary value problem with a sign changing nonlinear term lu t h t f t u 0 0 is a sign changing continuous function and may be unbounded from below by applying the topological degree of a completely continuous field and the first eigenvalue and its corresponding eigenfunction of a special linear operator some new results on the existence of nontrivial solutions for the above singular m point boundary value problem are obtained an example is then given to demonstrate the application of the main results the work improves and generalizes the main results of g han y wu nontrivial solutions of singular two point boundary value problems with sign changing nonlinear terms j math anal appl 325 2007 1327 1338 j sun g zhang nontrivial solutions of singular superlinear sturm liouville problem j math anal appl 313 2006 518 536

stabilized finite element formulation for elastic plastic finite deformations abstract this paper presents a stabilized finite element formulation for nearly incompressible finite deformations in hyperelastic plastic solids such as metals an updated lagrangian finite element formulation is developed where mesh dependent terms are added to enhance the stability of the mixed finite element formulation this formulation circumvents the restriction on the displacement and pressure fields due to the babuska brezzi condition and provides freedom in choosing interpolation functions in the incompressible or nearly incompressible limit typical in metal forming applications moreover it facilitates the use of low order simplex elements i e p1 p1 reducing the degrees of freedom required for the solution in the incompressible limit when stable elements are necessary linearization of the weak form is derived for implementation into a finite element code numerical experiments with p1 p1 elements show that the method is effective in incompressible conditions and can be advantageous in metal forming analysis

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

application of a novel time delayed polynomial grey model to predict the natural gas consumption in china the government of china is now trying to use natural gas as partial substitute of other fuels such as coal and gasoline developing the natural gas industry has been written in the 13th five year plan of china which is the most important official policy of china predicting the natural gas consumption comes to be very important for the government and energy companies to make decisions in this paper we propose a novel time delayed polynomial grey prediction model which is abbreviated as tdpgm 1 1 based on the grey system theory to forecast the natural gas consumption of china in comparison with the commonly used prediction models the data from 1995 to 2004 are used to build the prediction models and the data from 2005 to 2013 are used to assess the modelling accuracy the results show that the tdpgm 1 1 model outperforms the other models finally the tdpgm 1 1 model is used to forecast the natural gas consumption of china from 2014 to 2020 and different results from the previous research results have been obtained

existence theorems for a second order three point boundary value problem abstract letf 0 1 r 2 r be continuous ande c 0 1 let i 0 1 ai r all of theai s having the same sign i 1 2 m 2 0 x t f t x t x t e t t 0 1 e x 0 0 x 1 i 1 m 2 a i x i bc m we discuss existence theorems for the problem e bcm under some sign condition offabout the origin our analysis is based on a nonlinear alternative of leray schauder

stabilized finite element method for viscoplastic flow formulation with state variable evolution a stabilized mixed finite element formulation for modelling viscoplastic flow which can be used to model approximately steady state metal forming processes is presented the mixed formulation is expressed in terms of the velocity pressure and state variable fields where the state variable is used to describe the evolution of the material s resistance to plastic flow the resulting system of equations has two sources of well known instabilities one due to the incompressibility constraint and one due to the convection type state variable equation both of these instabilities are handled by adding mesh dependent stabilization terms which are functions of the euler lagrange equations to the usual galerkin method linearization of the weak form is derived to enable a newton raphson implementation into an object oriented finite element framework a progressive solution strategy is used for improving convergence for highly non linear material behaviour typical for metals numerical experiments using the stabilization method with hierarchic shape functions for the velocity pressure and state variable fields in viscoplastic flow and metal forming problems show that the stabilized finite element method is effective and efficient for non linear steady forming problems finally the results are discussed and conclusions are inferred

multiple solutions of singular three point boundary value problems on 0 abstract in this paper we study the existence of single and multiple solutions of three point boundary value problems for the following nonlinear singular second order differential equations x t p x t q x t h t f t x t 0 t 0 a x 0 b x 0 k x c 0 lim t x t e r t d 0 where p b 0 a k 0 q 0 0 r 0 p p 2 4 q 2 h 0 0 is continuous and may be singular at t 0 f 0 0 is continuous and may take a negative value by applying the technique of lower and upper solutions and the theory of topological degree we obtain the conditions for the existence of at least one solution and at least three solutions respectively

parameter optimization of nonlinear grey bernoulli model using particle swarm optimization abstract nonlinear grey bernoulli model ngbm is a novel grey forecasting model which is a simple modification of gm 1 1 together with bernoulli differential equation this paper presents a new parameter optimization scheme of ngbm using the particle swarm optimization pso algorithm the power index of bernoulli differential equation and production coefficient of the background value are considered as decision variables and the forecasting error is taken as the optimization objective parameter optimization of ngbm is formulated as the combinatorial optimization problem and would be solved collectively using pso technique once the pso finds the optimal parameters of ngbm the model can be optimized ngbm with this parameter optimization algorithm is then applied in long term power load forecasting results show that ngbm has remarkably improved the forecasting accuracy and pso is an effective global optimization algorithm suitable for the parameter optimization of ngbm

solvability of second order nonlinear three point boundary value problems abstract we are interested in the existence of nontrivial solutions to the three point boundary value problem bvp u t f t u t 0 0 t 1 u 0 0 u 1 u u where 0 1 f t u c 0 1 r r and are real constants fixed point theorems and degree theory are frequently used to study such problems recently the authors demonstrated that in many situations the shooting method proves to be an effective approach often leading to better results with shorter proofs here we present another such example assume that f t 0 0 and that there exist nonnegative functions k h l 1 0 1 such that f t w k t w h t for all t w 0 1 r sun and liu 13 for the special case 0 and sun 14 for the special case 0 showed that if the l 1 norm k 1 is sufficiently small then there exists a nontrivial solution to the bvp in this paper their results are improved using the shooting method

positive solutions of a nonlinear three point boundary value problem in this paper by using krasnoselskii s fixed point theorem in a cone we study the existence of single and multiple positive solutions to the three point boundary value problem bvp y t a t f y t 0 0

isogeometric residual minimization igrm for non stationary stokes and navier stokes problems abstract we show that it is possible to obtain a linear computational cost fem based solver for non stationary stokes and navier stokes equations our method employs a technique developed by guermond and minev 2011 which consists of singular perturbation plus a splitting scheme while the time integration schemes are implicit we use finite elements to discretize the spatial counterparts at each time step we solve a pde having weak derivatives in one direction only which allows for the linear computational cost at the expense of handling strong second order derivatives of the previous time step solution on the right hand side of these pdes this motivates the use of smooth functions such as b splines for high reynolds numbers some of these pdes become unstable to deal robustly with these instabilities we propose to use a residual minimization technique we test our method on problems having manufactured solutions as well as on the cavity flow problem

solvability of a three point nonlinear boundary value problem for a second order ordinary differential equation in case f x u u ps x p x u pjx u with pk 0 l 4 r locally integrable the boundary value problem l lt 1 2 was studied by kiguradze and lomtatidze i the purpose of this paper is to obtain existence and uniqueness theorems for the boundary value problem 1 1 t 1 2 under natural conditions on f using degree theoretic arguments we note that if u is a solution of 1 1 1 2 then there exists at least one 5 e q l such that u c 0 accordingly the boundary value problem

stabilized mixed finite element formulations for materially nonlinear partially saturated two phase media standard and enhanced bbar or eas low order finite elements applied to the problem of consolidation of two phase nonlinear continua do not satisfy the lbb condition when the same interpolation functions are used for both displacement and pore pressure fields strong spatial pressure oscillations are the main consequence of the lbb condition violation the class of direct stabilized methods widely used in the field of fluid mechanics is a powerful tool to circumvent violation of the aforementioned condition three stabilized formulations designed for the problem of consolidation of fully or partially saturated media are presented galerkin least squares gls with the least squares term construction based on the residuum of the local fluid mass conservation equation the pressure stabilized formulation fpl in which the rate of the pore pressure laplacian residual free in the incompressibility limit is added to the fluid mass conservation equation and finally a stabilized formulation in which the stabilization term is constructed based on the rate of the residuum of the local momentum equation an h convergence study and test problems for the three stabilized schemes are discussed

a generalized galerkin method for steady convection diffusion problems with application to quadratic shape function elements abstract a generalization of the standard galerkin finite element method is considered to enable it to deal successfully with steady convection diffusion problems the proposed method employs a generalized governing equation which is obtained by subtracting from the original differential equation the scalar product of its gradient by a vector of free parameters associated with each of the coordinate directions the generalized equation is successively discretized by the standard bubnov galerkin finite element method the effectiveness of the method is illustrated for the case of quadratic local interpolations in one and two space dimensions

stabilized finite element method for viscoplastic flow formulation and a simple progressive solution strategy abstract this paper presents a stabilized finite element formulation for steady state viscoplastic flow and a simple strategy for solving the resulting non linear equations with a newton raphson algorithm an eulerian stabilized finite element formulation is presented where mesh dependent terms are added element wise to enhance the stability of the mixed finite element formulation a local reconstruction method is used for computing derivatives of the stress field needed when higher order elements are used linearization of the weak form is derived to enable a newton raphson solution procedure of the resulting non linear equations in order to get convergence in the newton raphson algorithm a trial solution is needed which is within the radius of convergence an effective strategy for progressively moving inside the radius of convergence for highly non linear viscoplastic constitutive equations typical of metals is presented numerical experiments using the stabilization method with both linear and quadratic shape functions for the velocity and pressure fields in viscoplastic flow problems show that the stabilized method and the progressive convergence strategy are effective in non linear steady forming problems finally conclusions are inferred and extensions of this work are discussed

a stabilized mixed finite element method for finite elasticity formulation for linear displacement and pressure interpolation abstract a stabilized mixed finite element method for finite elasticity is presented the method circumvents the fulfillment of the ladyzenskaya babuska brezzi condition by adding mesh dependent terms which are functions of the residuals of the euler lagrange equations to the usual galerkin method the weak form and the linearized weak form are presented in terms of the reference and current configuration numerical experiments using a tetrahedral element with linear shape functions for the displacements and for the pressure show that the method successfully yields a stabilized element

a research on the deterministic grey dynamic model with multiple inputs dgdmmi 1 1 1 accumulated generating operation ago is one of the most important characteristics of grey theory and the purpose of ago is to reduce the randomness of the data the incompleteness of messages is the primary characteristic of grey theory and it is necessary to whiten a system by way of inserting more messages in the system the new model presented in this article is called the deterministic grey dynamic model with multiple inputs abbreviated as dgdmmi 1 1 1 additional several series can be introduced to act as the leading indicators input series except the predicted series output series by dgdmmi 1 1 1 model the messages for a system can be inserted sufficiently a transfer function model would be used to combine the ago series of input series with that of output series and then the deterministic convergence scheme is used to evaluate the unbiased estimates of the system parameters the relationship between input series and output series is erected sufficiently by dgdmmi 1 1 1 and high prediction accuracy of a dynamic system can be obtained then high prediction accuracy of economy and indirect measurement of engineering quantities can be broadly anticipated

an absolutely stabilized finite element method for the stokes problem on presente une formulation a elements finis absolument stabilisee pour le probleme de stokes on etablit des estimations d erreurs optimales dans la norme l 2 pour l approximation des champs de vitesses et de pressions

a research on the grey prediction model gm 1 n abstract the grey theory can be applied in the research of prediction decision making and control especially in prediction the primary characteristic of a grey system is the incompleteness of information a grey system could be whitened by way of inserting more messages in itself and its accuracy of prediction could be raised the solution to the existing grey prediction model gm 1 n is inaccurate and then its prediction accuracy cannot be expected to solve the existing gm 1 n by assuming step by step the first order accumulated generating operation data of the associated series to be constants is incorrect the existing model gm 1 n is seriously wrong even for a system having a nonnegative associated series with constant entries there are currently only a few wrong papers based on the existing gm 1 n model to be published almost all the improved prediction models based on the existing gm 1 n model are correct for example the improved models are correct by convolution integral or fitting their forcing terms by several elementary functions the algorithm of gmc 1 n is applied to explain why the existing gm 1 n model is incorrect in this article

fully automatic hp adaptive finite element method for the stokes problem in two dimensions abstract the paper is devoted to the solution of the stokes problem using a self adaptive hp finite element method hp fem in two dimensions the hp fem generates a sequence of optimal hp refined meshes delivering exponential convergence rates of the numerical error with respect to the number of degrees of freedom and cpu time optimal meshes are generated by performing a sequence of h and p refinements on an initial mesh provided by the user the hp strategy is based on the coarse fine grid paradigm and the minimization of the projection based interpolation pbi error we employ the hughes franca stabilization method for the stabilization of mixed problem with equal order elements

a better consistency for low order stabilized finite element methods abstract the standard implementation of stabilized finite element methods with a piece wise function space of order lower than the highest derivative present in the partial differential equation often suffers from a weak consistency that can lead to reduced accuracy the popularity of these low order elements motivates the development of a new stabilization operator which globally reconstructs the derivatives not present in the local element function space this new method is seen to engender a stronger consistency leading to better convergence and improved accuracy applications to the navier stokes equations are given which illustrate the improvement at a negligible additional cost

multiple positive solutions for m point boundary value problems with a one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for the one dimensional p laplacian p u q t f t u 0 t 0 1 subject to the boundary conditions u 0 i 1 m 2 a i u i u 1 i 1 m 2 b i u i where p s s p 2 s by using a fixed point theorem in a cone we present sufficient conditions for the existence of multiple positive solutions for the above boundary value problem

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

implicit finite incompressible elastodynamics with linear finite elements a stabilized method in rate form abstract we propose a stabilization method for linear tetrahedral finite elements suitable for the implicit time integration of the equations of nearly and fully incompressible nonlinear elastodynamics in particular we derive and discuss a generalized framework for stabilization and implicit time integration that can comprehensively be applied to the class of all isotropic hyperelastic models in this sense the presented development can be considered an important extension and complement to the stabilization approach proposed by the authors in previous work which was instead focused on explicit time integration and simple neo hookean models for nearly incompressible elasticity with the goal of computational efficiency we also present a two step block gauss seidel strategy for the time update of displacements velocities and pressures specifically a mixed system of equations for the velocity and pressure is updated implicitly in a first stage and the displacements are updated explicitly in a second stage the proposed mixed formulation is then embedded in newton type strategies for the nonlinear solution of the equations of motion various implicit time integration strategies are considered and particularly we focus on high frequency dissipation time integrators which are preferable in transient mechanics applications an extensive set of numerical computations with linear tetrahedral elements is presented to demonstrate the performance of the proposed approach

positive solution for singular boundary value problems abstract a sufficient condition for the existence of positive solutions of the nonlinear boundary value problem u t f t u t 0 0 u 0 u 1 0 is constructed where f 0 1 0 0 is continuous f t u is locally lipschitz continuous and f t u u is strictly decreasing in u 0 for each t 0 1

positive solutions for singular systems of three point boundary value problems this paper investigates the following singular systems of nonlinear second order three point boundary value problems u f t v email protected 0 1 v g t u email protected 0 1 u 0 v 0 0 u 1 email protected h v 1 email protected h where email protected 0 1 0 email protected 1 f and g may be singular at t 0 and or t 1 under some weaker conditions the existence of positive solutions is obtained by applying the fixed point theorem of cone expansion and compression two examples are then presented to demonstrate the application of our main results

grey dynamic input output analysis abstract a system whose information is partially known and partially unknown is named as a grey system and it is general situation in reality on the basis of grey number matrix and their covered operation some definitions of grey functions are enumerated combining grey system theory with traditional dynamic input output analysis we propose the grey dynamic input output analysis it has two types i e the continuous and the disperse the most important results are the computational formulas of the matrix covered set of inverse grey investment coefficient matrix by using them we can forecast and control the economic system under the uncertain situation for the calculation of the matrix covered set of inverse grey matrices we obtain the desired formulas which can be applied to general grey matrices the formulas can greatly promote the development of grey theory and enrich the applied fields of uncertain mathematics the modified case illustrates our method

a nonlinear grey forecasting model with double shape parameters and its application abstract the solution of bernoulli differential equation can be described as a generalized logistic curve function weibull cumulative distribution function is also an analytic solution of one variable coefficient differential equation but however because of the exact analytical solution problem of the equation up to now the developing coefficient of all the grey forecasting models is still defined as a constant so the aim of this paper is just to construct a novel grey differential equation model by combining ngbm 1 1 and weibull cumulative distribution function the proposed model wbgm 1 1 has the advantages of ngbm 1 1 and weibull cumulative distribution where there are double shape parameters the developing coefficient of the grey forecasting model is extended to be a variant property analysis of wbgm 1 1 shows that the fitting accuracy is higher and the applicable confines are wider finally this paper gives an optimization method for the parameters of wbgm 1 1 a classic example and a practical case are studied for confirming the effectiveness of wbgm 1 1 the case study is the prediction for the number of invention patents of integrated circuit ic filed in china from 2007 to 2017 results of the example and case study are compared to other forecasting models including gm 1 1 ngbm 1 1 holt exponential smoothing and arima results show that wbgm 1 1 is a more general and more efficient model in grey prediction theory

positive solutions for third order sturm liouville boundary value problems with p laplacian in this paper by using the fixed point index method we establish the existence of at least one or at least two positive solutions for the third order sturm liouville boundary value problem with p laplacian f p u t f t u t 0 email protected 0 1 au 0 email protected 0 0 cu 1 email protected 1 0 u 0 0 where f p s s p 2s p 1 as an application an example is given to demonstrate the main result

on the orthogonal subgrid scale pressure stabilization of finite deformation j2 plasticity the use of stabilization methods is becoming an increasingly well accepted technique due to their success in dealing with numerous numerical pathologies that arise in a variety of applications in computational mechanics in this paper a multiscale finite element method technique to deal with pressure stabilization of nearly incompressibility problems in nonlinear solid mechanics at finite deformations is presented a j2 flow theory plasticity model at finite deformations is considered a mixed formulation involving pressure and displacement fields is used as starting point within the finite element discretization setting continuous linear interpolation for both fields is considered to overcome the babuska brezzi stability condition a multiscale stabilization method based on the orthogonal subgrid scale osgs technique is introduced a suitable nonlinear expression of the stabilization parameter is proposed the main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements which are easy to generate and therefore very convenient for practical industrial applications numerical results obtained using the osgs stabilization technique are compared with results provided by the p1 standard galerkin displacements linear triangular tetrahedral element p1 p1 standard mixed linear displacements linear pressure triangular tetrahedral element and q1 p0 mixed bilinear trilinear displacements constant pressure quadrilateral hexahedral element for 2d 3d nearly incompressible problems in the context of a nonlinear finite deformation j2 plasticity model

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

positive solutions of singular three point boundary value problems for the one dimensional p laplacian abstract we use the fixed point index theory to establish the existence of at least one or two positive solutions for the singular three point boundary value problems f p y a t f y t 0 0

stabilized shock hydrodynamics i a lagrangian method abstract a new supg stabilized formulation for lagrangian hydrodynamics of materials satisfying mie gruneisen equation of state is proposed it allows the use of simplex type triangular tetrahedral meshes as well as the more commonly used brick type quadrilateral hexahedral meshes the proposed method yields a globally conservative formulation in which equal order interpolation p1 or q1 isoparametric finite elements is applied to velocities displacements and pressure as a direct consequence and in contrast to traditional cell centered multidimensional hydrocode implementations the proposed formulation allows a natural representation of the pressure gradient on element interiors the supg stabilization involves additional design requirements specific to the lagrangian formulation a discontinuity capturing operator in the form of a noh type viscosity with artificial heat flux is used to preserve stability and smoothness of the solution in shock regions a set of challenging shock hydrodynamics benchmark tests for the euler equations of gas dynamics in one and two space dimensions is presented in the two dimensional case computations performed on quadrilateral and triangular grids are analyzed and compared these results indicate that the new formulation is a promising technology for hydrocode applications

positive solutions of a nonlinear three point boundary value problem in this paper by using the fixed point index theorems we study the existence of at least one or two positive solutions to the three point boundary value problem y t a t f y t 0 0 t 1 y 0 0 y 1 y where 0 1 0 1 as an application we also give some examples to demonstrate our results

improvement of the flow formulation by recovery of the hydrostatic pressure using the finite point method most of the existing numerical methods based on penalty technique lead to pressure fields which are not satisfactory especially when crude meshes are used the present work for the first time using a simple and effective finite point approach approximates the total hydrostatic stresses by this new technique the nodal hydrostatic pressure values are calculated so that the gradient of hydrostatic pressure satisfies the equilibrium equation with regard to the current distribution of deviatoric stresses this approach is verified using a cantilever beam with known analytical stress field it is also applied to a typical 2d axisymmetric bulk metal forming process the calculated pressure field is then compared with available solutions the results of the present approach are very encouraging copyright 2005 john wiley sons ltd

positive solutions for nonlinear three point boundary value problems on time scales abstract let t be a time scale such that 0 t t consider the following three point boundary value problem on time scales u t a t f t u t 0 t 0 t u 0 u 0 0 u u t where 0 0 0 t 0 t and d t 1 0 by using fixed point theorems in cones some new and general results are obtained for the existence of single and multiple positive solutions of the above problem in particular our criteria generalize and improve some known results

a new family of stable elements for nearly incompressible elasticity based on a mixed petrov galerkin finite element formulation adding to the classical hellinger reissner formulation another residual form of the equilibrium equation a new petrov galerkin finite element method is derived it fits within the framework of a mixed finite element method and is proved to be stable for rather general combinations of stress and displacement interpolations including equal order discontinuous stress and continuous displacement interpolations which are unstable within the galerkin approach error estimates are presented using the babuska brezzi theory and numerical results confirm these estimates as well as the good accuracy and stability of the method

an adaptive descent method for non linear viscoplasticity a forming model based on a viscoplastic flow formulation is derived which includes the effects of small elastic strains a significant feature of the formulation is its reliance on the dominant inelastic material characteristics in the formation of the stiffness matrix for large strain problems the resultant non linear system of equations is solved by an adaptive descent method which combines the rapid convergence of newton s method near the solution with the robustness of a method of successive approximations the use of the adaptive descent method effectively extends the viscoplastic flow formulations into the nearly rate insensitive range of behaviours exhibited for example by metals at low temperature where slow convergence of the non linear solution algorithm has traditionally hampered their use

positive solutions to a generalized second order three point boundary value problem abstract in this paper by using krasnoselskii fixed point theorem we study the existence of at least or two positive solutions to the nonlinear second order three point boundary value problem y t a t f y t 0 0 t t y 0 y y t y where 0 t 0 t 0 t t are given constants as an application we also give some examples to demonstrate our results

positive solutions of a nonlinear four point boundary value problems in this paper by using the krasnoselskii s theorem in a cone we study the existence of at least one or two positive solutions to the four point boundary value problemy t a t f y t 0 00 as an application we also give some examples to demonstrate our results

a sharper condition for the solvability of a three point second order boundary value problem letf 0 1 r2 rbe a function satisfying caratheodory s conditions ande t l1 0 1 let 0 1 r 1 1 be given this paper is concerned with the problem of existence of a solution for the three point boundary value problem formula omitted this problem was studied earlier by gupta ntouyas and tsamatos when 1 and when 1 with 1 in the general case this problem was studied by gupta as a multi point boundary value problem in this paper sharper existence conditions are obtained for the solvability of the above boundary value problem in the general case

a velocity stress mixed stabilized nodal finite element for elastodynamics analysis and computations with strongly and weakly enforced boundary conditions abstract a new nodal mixed finite element is proposed for the simulation of linear elastodynamics and wave propagation problems in time domain our method is based on equal order interpolation discrete spaces for both the velocity or displacement and stress or strain tensor variables the mixed form is derived using either the velocity stress or velocity strain pair of unknowns the latter being instrumental in extensions of the method to nonlinear mechanics the proposed approach works equally well on hexahedral or tetrahedral grids and for this reason it is suitable for time domain engineering applications in complex geometry the peculiarity of the proposed approach is the use of the rate form of the stress update equation which yields a set of governing equations with the structure of a non dissipative space time friedrichs system we complement standard traction boundary conditions for the stress with strongly and weakly enforced boundary conditions for the velocity or displacement weakly enforced boundary conditions are particularly suitable when considering complex geometrical shapes because they do not require dedicated data structures for the imposition of the boundary degrees of freedom but rather they utilize the structure of the variational formulation we also show how the framework of weakly enforced boundary conditions can be used to develop variational forms for multi domain simulations of heterogeneous media a complete analysis including stability and convergence proofs is included in the case of a space time variational approach a series of computational tests are used to demonstrate and verify the performance of the proposed approach

positive solutions to a type of nonlinear three point boundary value problem with sign changing nonlinearities in this paper by using krasnoselskii s fixed point theorem in a cone we study the existence of positive solutions for the second order three point boundary value problem u t a t u t lf t u t 0 0

revisiting stabilized finite element methods for the advective diffusive equation we give a brief overview of stabilized finite element methods and illustrate the developments applied to the advection diffusion equation this article presents a concise perspective of the developments emanated from the works started in the 1980s through today 2005 elsevier b v all rights reserved pacs 47 11 j

positive solutions of second order three point boundary value problems with change of sign we study the existence of positive solutions of the second order three point boundary value problems t a t f y t 0 0 t 1 y 0 0 y 1 y n where 0 1 0 1 we show the existence of at least one positive solution by applying the krasnoselskii fixed point theorem in a cone here a t is allowed to changes sign on 0 1 applications of our results are provided to yield positive radial solutions of some elliptic boundary value problems on an annulus

asymptotic solutions for a second order differential equation with three point boundary conditions abstract in this paper we are concerned with the following singularly perturbed second order three point boundary value problem 1 1 y 2 q 1 x q 2 x y 0 1 1 2 y 0 a y 1 y where 0

application of a novel nonlinear multivariate grey bernoulli model to predict the tourist income of china abstract the nonlinear grey bernoulli model which is often called the ngbm 1 1 appeals considerable interest of research due to its effectiveness in time series forecasting the success of the ngbm 1 1 model proves that the nonlinear bernoulli equation can be efficient to build grey prediction models this paper is mainly aiming at building a more general nonlinear grey prediction model based on the bernoulli equation and the modelling procedures of the gmc 1 n which is called the nonlinear grey bernoulli multivariate model abbreviated as the ngbmc 1 n the ngbmc 1 n can be converted to the ngbm 1 1 and the gmc 1 n with different power parameters thus it can be regarded as an extension of these models two case studies of forecasting the domestic income and foreign currency earning have been carried out to validate the effectiveness of the ngbmc 1 n model comparing to the novel linear multivariate grey models including the gmc 1 n dgm 1 n and rdgm 1 n and the classical arima model the advantages of the ngbmc 1 n model in nonlinear time series forecasting over the existing linear models have been shown in the numerical results

multiple positive solutions of four point nonlinear boundary value problems for a higher order p laplacian operator with all derivatives abstract in this paper we study the existence of multiple positive solutions for nonlinear four point boundary value problems for a higher order p laplacian operator with all derivatives some new results are obtained for the multiplicity of positive solutions by applying the avery henderson fixed point theorem and the leggett williams fixed point theorem in a cone which is different from the previous approaches

hp version discontinuous galerkin methods for hyperbolic conservation laws abstract the development of hp version discontinuous galerkin methods for hyperbolic conservation laws is presented in this work a priori error estimates are derived for a model class of linear hyperbolic conservation laws these estimates are obtained using a new mesh dependent norm that reflects the dependence of the approximate solution on the local element size and the local order of approximation the results generalize and extend previous results on mesh dependent norms to hp version discontinuous galerkin methods a posteriori error estimates which provide bounds on the actual error are also developed in this work numerical experiments verify the a priori estimates and demonstrate the effectiveness of the a posteriori estimates in providing reliable estimates of the actual error in the numerical solution

positive solutions for singular second order three point boundary value problems abstract in this paper the singular three point boundary value problem u t h t f t u 0 0 t 1 u 0 0 u 1 u where 0 1 0 1 is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear operator h t is allowed to be singular at t 0 1 and f may be singular at u 0 the existence of a positive solution is obtained by a fixed index point

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100