simulation of the transient behavior of a one dimensional semiconductor device ii a numerical method based on treating the potential by a mixed finite element method and the electron and hole density equations by a finite element version of a modification of the method of characteristics is introduced to simulate the transient behavior of a semiconductor device for which the dependence of the coefficients of the conductivity equations on the electric field is considered and the einstein relations are not assumed l 2 error estimates that are independent of l infty error estimates for the approximate electric field are derived for a single space variable model

an algebraic approximation for the matrix exponential in singularly perturbed boundary value problems a symmetric difference scheme for linear stiff or singularly perturbed boundary value problems of first order with constant coefficients is constructed being based on a stability function containing a matrix square root its essential feature is the unconditional stability in the absence of purely imaginary eigenvalues of the coefficient matrix local damping of errors uniform stability and uniform second order convergence are proved the computation of the specific matrix square root by a well known stable variant of newton s method is discussed a numerical example confirming the results is given

entropy estimate of a probability density from its mellin transform entropy estimate of heavy tailed probability distribution from its mellin transform is considered such an estimate is provided uniquely in terms of expected values obtained from mellin transform some particular cases are analytically investigated as a low number of expected values are available

on the initial boundary value problem for the bipolar hydrodynamic model for semiconductors abstract the global existence and zero relaxation limit results of weak solutions of the initial boundary value problem to the bipolar hydrodynamic model for semiconductors are established by the theory of compensated compactness the boundary conditions of weak solutions in the sense of traces are discussed

application of the mesh independence principle to mesh refinement the mesh independence principle mip for a newton iteration applied to an operator equation and its discretization for different stepsizes h states for a fixed starting point the number of iterations of newton s method to obtain a fixed tolerance is eventually independent of h this mip is used to formulate an efficient strategy for the solution of nonlinear equations amounting to the work equivalent of two or three newton iterates for the smallest h examples are given

asynchronous parallel successive overrelaxation for the symmetric linear complementarity problem convergence is established for asynchronous parallel successive overrelaxation sor algorithms for the symmetric linear complementarity problem for the case of a strictly diagonally dominant matrix convergence is achieved for a relaxation factor interval of 0 2 with line search and 0 1 without line search computational tests on the sequent symmetry s81 multiprocessor give speedup efficiency in the 43 91 range for the cases for which convergence is established the tests also show superiority of the asynchronous sor algorithms over their synchronous counterparts

spline based computational technique for linear singularly perturbed boundary value problems a fourth order difference scheme via cubic spline in compression for singularly perturbed two point boundary value problems of the form ey p x y q x y r x y a a y b bis presented the convergence analysis is given finally computational efficiency of the method is verified through numerical examples

quasineutral limit of a time dependent drift diffusion poisson model for p n junction semiconductor devices abstract in this paper the vanishing debye length limit of the bipolar time dependent drift diffusion poisson equations modelling insulated semiconductor devices with p n junctions i e with a fixed bipolar background charge is studied for sign changing and smooth doping profile with good boundary conditions the quasineutral limit zero debye length limit is performed rigorously by using the multiple scaling asymptotic expansions of a singular perturbation analysis and the carefully performed classical energy methods the key point in the proof is to introduce a density transform and two weighted liapunov type functionals first and then to establish the entropy production integration inequality which yields the uniform estimate with respect to the scaled debye length the basic point of the idea involved here is to control strong nonlinear oscillation by the interaction between the entropy and the entropy dissipation

collocation methods for boundary value problems on long intervals this paper deals with the numerical solution of boundary value problems of ordinary differential equations posed on infinite intervals we cut the infinite interval at a finite large enough point and insert additional so called asymptotic boundary conditions at the far right end and then solve the resulting two point boundary value problem by an a stable symmetric collocation method problems arise because standard theory predicts the use of many grid points as the length of the interval increases using the exponential decay of the infinite solution an asymptotic a priori mesh size sequence which increases exponentially and which therefore only employs a reasonable number of meshpoints is developed and stability as the length of the interval tends to infinity is shown we also show that the condition number of the collocation equations is asymptotically proportional to the number of meshpoints employed when using this exponentially graded mesh using k stage collocation at gaussian points and requiring an accuracy 0 e at the knots implies that the number of meshpoints is q g i 2k as e o 0

a mixed method for the mixed initial boundary value problems of equations of semiconductor devices in this article the approximation of nonstationary equations of the semiconductor device with mixed boundary conditions is considered the approximate procedure of this system using a galerkin method that makes use of a mixed finite element method for the potential equation combined with a finite element method for the concentration equations is presented due to the poor regularity properties of the solutions to the semiconductor equations caused by mixed boundary conditions a nonstandard analysis for the semidiscrete galerkin procedure is used existence and uniqueness of the approximate solution is proved a convergence analysis is also given for the method

success or failure of a firm under different financing policies a dynamic stochastic model abstract the value of a firm evolves in time according to a standard ito s stochastic differential equation and under different types of financial support in particular both the cases of legal and illegal financing are considered the ruin success probabilities for the firm are evaluated in closed form via special functions in the various settings some functionals of the process which are relevant from the viewpoint of the financiers via kac s lemma are shown to obey a pde which is studied both with analytic tools second order odes of hypergeometric type and with numerical ones the case of insufficient payments is analyzed via stochastic calculus and a new model for loan renegotiation is offered

on spline basis selection for solving differential equations the suitability of b splines as a basis for piecewise polynomial solution representation for solving differential equations is challenged two alternative local solution representations are considered in the context of collocating ordinary differential equations hermite type and lmonomial both are much easier and shorter to implement and somewhat more efficient than b splines a new condition number estimate for the b splines and hermite type representations is presented one choice of the hermite type representation is experimentally determined to produce roundoff errors at most as large as those for b splines the monomial representation is shown to have a much smaller condition number than the other ones and correspondingly produces smaller roundoff errors especially for extremely nonuniform meshes the operation counts for the two local representations considered are about the same the hermite type representation being slightly cheaper it is concluded that both representations are preferable

two step modulus based matrix splitting iteration method for a class of nonlinear complementarity problems abstract in this paper we reformulate the nonlinear complementarity problem as an implicit fixed point equation we establish a modulus based matrix splitting iteration method based on the implicit fixed point equation and prove its convergence theorem under suitable conditions furthermore we propose a two step modulus based matrix splitting iteration method which may achieve higher computing efficiency we can obtain many matrix splitting iteration methods by suitably choosing the matrix splittings and the parameters the proposed methods can be regarded as extensions of the methods for linear complementarity problem numerical experiments are presented to show the effectiveness of the proposed methods

stieltjes moment problem via fractional moments stieltjes moment problem is considered to recover a probability density function from the knowledge of its infinite sequence of ordinary moments the approximate density is obtained through maximum entropy technique under the constraint of few fractional moments the latter are numerically obtained from the infinite sequence of ordinary moments and are chosen in such a way as to convey the maximum information content carried by the ordinary moments as a consequence a model with few parameters is obtained and intrinsic numerical instability is avoided it is proved that the approximate density is useful for calculating expected values and some other interesting probabilistic quantities

on strongly reverse biased semiconductor diodes a singular perturbation analysis of the drift diffusion model for stationary flow of charge carriers in a semiconductor device is given an extension of earlier results provides deeper insight into the structure of the solution and the possibility of computing approximations for leakage currents the solvability of the approximating problem is proved

conditioning of the steady state semiconductor device problem when solving numerically the steady state semiconductor device problem using appropriate discretizations extremely large condition numbers are often encountered for the linearized discrete device problem these condition numbers are so large that if they represented a sharp bound on the amplification of input errors or even of roundoff errors then the obtained numerical solution would be meaningless as it turns out one major reason for these large numbers is due to poor row and column scaling which is essentially harmless and or can be fixed but another reason could be an ill conditioned device which yields a true loss of significant digits in the numerical calculation in this paper we carry out a conditioning analysis for the steady state device problem we consider various quasilinearizations as well as gummel type iterations and obtain stability bounds which may indeed allow ill conditioning in general these bounds are exponential in the potential variation and are sharp e g for a thyristor but for devices where each smooth subdomain has an ohmic contact e g a pn diode moderate bounds guaranteeing well conditioning are obtained moreover the analysis suggests how various row and column scalings should be applied in order for the measured condition numbers to correspond more realistically to the true loss of significant digits in the calculations

stability of collocation at gaussian points symmetric runge kutta schemes are particularly useful for solving stiff two point boundary value problems such a stable schemes perform well in many cases but it is demonstrated that in some instances the stronger property of algebraic stability is required a characterization of symmetric algebraically stable runge kutta schemes is given the class of schemes thus defined turns out not to be very rich the only collocation schemes in it are those based on gauss points and other schemes in the class do not seem to offer any advantage over collocation at gaussian points

approximate solution of boundary value problems on infinite intervals by collocation methods on etudie la solution numerique approchee des problemes aux valeurs limites pour des equations differentielles sur des intervalles inifinis on utilise les methodes de collocation

the close relationships between methods for solving two point boundary value problems the well conditioning of a boundary value problem is shown to be related to bounding two quantities one involving the boundary conditions and the other involving the green s function in the case of a solution dichotomy they are related to known stability results these results easily explain why difficulties arise using superposition and reduced superposition it is shown how multiple shooting overcomes these difficulties by relating its matrix conditioning to the underlying boundary value problem some factorization methods for the multiple shooting method are considered these show the close relationships between multiple shooting the stabilized march and invariant imbedding and one factorization leads to an efficient new way to implement each of these three methods many of the results apply for collocation and finite difference methods too finally it is shown both theroetically and computationally when matrix compactification can lead to difficulty

finite element approximation to initial boundary value problems of the semiconductor device equations with magnetic influence we shall consider zlamal s approach to the nonstationary equations of the semiconductor device theory under magnetic fields with mixed boundary conditions owing to the reduced smoothness of the electric potential v and carrier densities n and p caused by considering the mixed boundary conditions we must use a nonstandard analysis for this procedure existence as well as uniqueness of the approximate solution is proved the convergence rates obtained in this paper are slower than those previously obtained for pure dirichlet or neumann boundary conditions

asynchronous parallel nonlinear multisplitting relaxation methods for large sparse nonlinear complementarity problems in accordance with the principle of sufficiently using delayed information and making use of the nonlinear multisplitting and the nonlinear relaxation techniques we present in this paper a class of asynchronous parallel nonlinear multisplitting successive overrelaxation sor methods for solving large sparse nonlinear complementarity problems on high speed mimd multiprocessor systems these new methods particularly include the so called asynchronous parallel nonlinear multisplitting sor newton method asynchronous parallel nonlinear multisplitting sor chord method and asynchronous parallel nonlinear multisplitting sor steffensen method under suitable conditions we establish the local convergence theory of this class of new methods numerical imitations show that our new methods are feasible and efficient for solving the nonlinear complementarity problems on the mimd multiprocessor systems

quasi neutral limit to the drift diffusion models for semiconductors with physical contact insulating boundary conditions abstract in this paper the limit of vanishing debye length in a bipolar drift diffusion model for semiconductors with physical contact insulating boundary conditions is studied in one dimensional case the quasi neutral limit zero debye length limit is proved by using the asymptotic expansion methods of singular perturbation theory and the classical energy methods our results imply that one kind of the new and interesting phenomena in semiconductor physics occurs

real moments from moments and vice versa positive and negative real moments are calculated uniquely in terms of given moments when the underlying stieltjes moment problem is determinate as well under weak hypothese moments are calculated from real moments the approximate densities which allow us to calculate real moments and moments reciprocally are borrowed from maximum entropy or minimun directed divergence techniques

high order finite element methods for singularly perturbed elliptic and parabolic problems we develop a framework for applying high order finite element methods to singularly perturbed elliptic and parabolic differential systems that utilizes special quadrature rules to confine spurious effects such as excess diffusion and nonphysical oscillations to boundary and interior layers this approach is more suited for use with adaptive mesh refinement and order variation techniques than other problem dependent methods quadrature rules developed for two point convection diffusion and reaction diffusion problems are used with finite element software to solve examples involving ordinary and partial differential equations numerical artifacts are confined to layers for all combinations of meshes orders and singular perturbation parameters that were tested radau or lobatto quadrature used with the finite element method to solve respectively convection and reaction diffusion problems provide the benefits of the specialized quadrature formulas and are simpler to implement

asymptotic and numerical analysis of singular perturbation problems a survey this paper is intended to be a brief survey of the asymptotic and numerical analysis of singular perturbation problems the purpose is to find out what problems are treated and what numerical asymptotic methods are employed with an eye toward the goal of developing general methods to solve such problems a summary of the results of some recent methods is presented and this leads to conclusions and recommendations about what methods to use on singular perturbation problems finally some areas of current research are indicated a bibliography of about 130 items is provided

moment information and entropy evaluation for probability densities abstract how much information does the sequence of integer moments carry about the corresponding unknown absolutely continuous distribution we prove that a reliable evaluation of the corresponding shannon entropy can be done by exploiting some known theoretical results on the entropy convergence uniquely involving exact moments without solving the underlying moment problem all the procedure essentially rests on the solution of linear systems with nearly singular matrices and hence it requires both calculations in high precision and a pre conditioning technique numerical examples are provided to support the theoretical results

a singularly perturbed boundary value problem modelling a semiconductor device this paper is concerned with the static one dimensional modelling of a semiconductor device namely the pn junction when a bias is applied the governing equations are the well known equations describing carrier transport in a semiconductor which consist of a system of ordinary differential equations subject to boundary conditions imposed at the contacts because of the different orders of magnitude of the solution components at the boundaries we scale the components individually and obtain a singular perturbation problem we analyse the equilibrium case zero bias applied and set up approximate models posed as singularly perturbed second order equations by neglecting the hole and electron current densities this makes sense for small forward bias and for moderate reverse bias for the full problem we prove an a priori estimate on the number of electron hole carrier pairs and derive asymptotic expansions as the perturbation parameter tends to zero by setting up the reduced system and the boundary

recovering a probability density function from its mellin transform the recovering of a probability density function f x from its mellin transform m s is considered the approximate f m x is chosen resorting to maximum entropy technique constrained by the first derivatives of m s evaluated at s 1 so the basic properties of a probability density are saved existence conditions of the approximate f m x entropy convergence and then l 1 norm convergence are proved some numerical examples are reported resorting to the mellin transform is an alternative to laplace one as the recovered probability distribution is heavy tailed or equivalently its probability density function has abscissa convergence laplace transform equal to 0

numerical inversion of the mellin transform on the real line for heavy tailed probability density functions a method for numerical inversion on the real line of the mellin transform without reduction of the problem to the inversion of laplace transform is described maximum entropy technique is invoked in choosing the analytical form of the approximant function entropy convergence and then l 1 norm convergence is proved a stability analysis in evaluating entropy and expected values is illustrated an upper bound of the error in the expected values computation is provided in terms of entropy

on the proximity of distributions in terms of coinciding fractional moments a bound on the absolute difference between two distributions based on entropy is introduced such a bound can be made as precise as desired according to the number of common fractional moments assumed the approximating distribution is obtained by maximizing the entropy constrained by fractional moments

comparison of time and spatial collocation methods for the heat equation we combine a high order compact finite difference scheme to approximate the spatial derivatives and collocation techniques for the time component to numerically solve the two dimensional heat equation we use two approaches to implement the time collocation methods the first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadratures we also implement a spatial collocation method where differential quadratures are utilized for spatial derivatives and an implicit scheme for marching in time we compare all the three techniques by studying their merits and analyzing their numerical performance our experiments show that all of them achieve high accurate approximate solution but the time collocation method with differential quadrature offers with respect to the one with explicit polynomials less computational complexity and a better efficiency all our computations based on parallel algorithms are carried out on the cray sv1

on collocation schemes for quasilinear singularly perturbed boundary value problems a numerical method for boundary value problems for quasilinear systems of singularly perturbed ordinary differential equations is presented the method is based on collocation with polynomial splines the stability properties of the associated difference operator are examined and a stepsize algorithm to achieve a certain over all accuracy is developed the number of gridpoints required by the algorithm is estimated

uniform high order difference schemes for a singularly perturbed two point boundary value problem on construit une famille de schemas aux differences finies uniformement precis pour le probleme du type eu a x u b x u f x on donne une analyse complete de l erreur de discretisation basee sur les resultats de stabilite on presente des essais numeriques

a class of parallel nonlinear multisplitting relaxation methods for the large sparse nonlinear complementarity problems abstract by making use of the nonlinear multisplitting and the nonlinear relaxation techniques we present in this paper a class of parallel nonlinear multisplitting successive overrelaxation methods for solving the large sparse nonlinear complementarity problems on the modern high speed multiprocessors these new methods particularly include the so called nonlinear multisplitting sor newton method under suitable conditions we establish the local convergence theories of the new methods and investigate their asymptotic convergence rates a lot of numerical results show that our new methods are feasible and efficient for parallel solving the nonlinear complementarity problems

an approximate newton method for the solution of the basic semiconductor device equations an iterative method for the solution of the steady state fundamental semiconductor device equations is presented and analyzed it is shown that while requiring the same amount of operations per iteration as gummel cycle iterations the new method has local convergence properties similar to those of newton s method

boundary value problems and dichotomic stability since the conditioning of a boundary value problem bvp is closely related to the existence of a dichotomic fundamental solution i e where one set of modes is increasing and a complementary set is decreasing it is important to have discretization methods that conserve this dichotomy property the conditions this imposes on such a method are investigated in this paper they are worked out in more detail for scalar second order equations the central difference scheme and for linear first order systems as well for the latter type both one step methods including collocation and multistep methods those that may be used in multiple shooting are examined

iterative methods for variational and complementarity problems in this paper we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems included among such methods are the newton and several successive overrelaxation algorithms for the most part the study is concerned with the family of linear approximation methods these are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches the paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria finally several convergence results are obtained for some nonlinear approximation methods

parallel nonlinear multisplitting methods linear multisplitting methods are known as parallel iterative methods for solving a linear systemax b we extend the idea of multisplittings to the problem of solving a nonlinear system of equationsf x 0 our nonlinear multisplittings are based on several nonlinear splittings of the functionf in a parallel computing environment each processor would have to calculate the exact solution of an individual nonlinear system belonging to his nonlinear multisplitting and these solutions are combined to yield the next iterate although the individual systems are usually much less involved than the original system the exact solutions will in general not be available therefore we consider important variants where the exact solutions of the individual systems are approximated by some standard method such as newton s method several methods proposed in literature may be regarded as special nonlinear multisplitting methods as an application of our systematic approach we present a local convergence analysis of the nonlinear multisplitting methods and their variants one result is that the local convergence of these methods is determined by an induced linear multisplitting of the jacobian off

numerical methods for singular perturbation problems consider the two point boundary value problem for a stiff system of ordinary differential equations an adaptive method to solve these problems even when turning points are present is discussed

electrical structures of interfaces a painleve ii model a painleve ii model derived out of the classical nernst planck system is applied in the context of boundary value problems that describe the electric field distribution in a region x 0 occupied by an electrolyte for privileged flux ratios of the ion concentrations the auto backlund transformation admitted by the painleve ii equation may be applied iteratively to construct exact solutions to classes of physically relevant boundary value problems these representations involve in turn either yablonskii vorob ev polynomials or classical airy functions the requirement that the electric field distribution and ion concentrations in these representations be non singular imposes constraints on the physical parameters these are investigated in detail along with asymptotic properties

on the numerical integration of nonlinear two point boundary value problems using iterated deferred corrections part 2 the development and analysis of highly stable deferred correction formulae iterated deferred correction methods have been very widely used for the numerical solution of general nonlinear two point boundary value problems in ordinary differential equations however there

a survey of numerical techniques for solving singularly perturbed ordinary differential equations this survey paper contains a surprisingly large amount of material and indeed can serve as an introduction to some of the ideas and methods of singular perturbation theory starting from prandtl s work a large amount of work has been done in the area of singular perturbations this paper limits its coverage to some standard singular perturbation models considered by various workers and the numerical methods developed by numerous researchers after 1984 2000 the work done in this area during the period 1905 1984 has already been surveyed by the first author of this paper see appl math comput 30 1989 223 for details due to the space constraints we have covered only singularly perturbed one dimensional problems

a class of asynchronous parallel nonlinear accelerated overrelaxation methods for the nonlinear complementarity problems in accordance with the principle of using sufficiently the delayed information and by making use of the nonlinear multisplitting and the nonlinear relaxation techniques we present in this paper a class of asynchronous parallel nonlinear multisplitting accelerated overrelaxation aor methods for solving the large sparse nonlinear complementarity problems on the high speed mimd multiprocessor systems these new methods in particular include the so called asynchronous parallel nonlinear multisplitting aor newton method the asynchronous parallel nonlinear multisplitting aor chord method and the asynchronous parallel nonlinear multisplitting aor steffensen method under suitable constraints on the nonlinear multisplitting and the relaxation parameters we establish the local convergence theory of this class of new methods when the jacobi matrix of the involved nonlinear mapping at the solution point of the nonlinear complementarity problem is an h matrix

the truncated stieltjes moment problem solved by using kernel density functions in this work the problem of the approximate numerical determination of a semi infinite supported continuous probability density function pdf from a finite number of its moments is addressed the target space is carefully defined and an approximation theorem is proved establishing that the set of all convex superpositions of appropriate kernel density functions kdfs is dense in this space a solution algorithm is provided based on the established approximate representation of the target pdf and the exploitation of some theoretical results concerning moment sequence asymptotics the solution algorithm also permits us to recover the tail behavior of the target pdf and incorporate this information in our solution a parsimonious formulation of the proposed solution procedure based on a novel sequentially adaptive scheme is developed enabling a very efficient moment data inversion the whole methodology is fully illustrated by numerical examples

collocation for singular perturbation problems i first order systems with constant coefficients the application of collocation methods for the numerical solution of singularly perturbed ordinary differential equations is investigated collocation at gauss radau and lobatto points is considered for both initial and boundary value problems for first order systems with constant coefficients particular attention is paid to symmetric schemes for boundary value problems these problems may have boundary layers at both interval ends br our analysis shows that certain collocation schemes in particular those based on gauss or lobatto points do perform very well on such problems provided that a fine mesh with steps proportional to the layers width is used in the layers only and a coarse mesh just fine enough to resolve the solution of the reduced problem is used in between ways to construct appropriate layer meshes are proposed of all methods considered the lobatto schemes appear to be the most promising class of methods as they essentially retain their usual superconvergence power for the smooth reduced solution whereas gauss legendre schemes do not br we also investigate the conditioning of the linear systems of equations arizing in the discretization of the boundary value problem for a row equilibrated version of the discretized system we obtain a pleasantly small bound on the maximum norm condition number which indicates that these systems can be solved safely by gaussian elimination with scaled partial pivoting

a note on proximity of distributions in terms of coinciding moments a bound on the absolute difference between two distributions based on entropy is introduced such a bound can be made as precise as desired according to the number of common moments assumed the approximating distribution is obtained by maximizing the entropy constrained by moments

the monotone convergence of a class of parallel nonlinear relaxation methods for nonlinear complementarity problems abstract we set up a class of parallel nonlinear multisplitting aor methods by directly multisplitting the nonlinear mapping involved in the nonlinear complementarity problems the different choices of the relaxation parameters can yield all the known and a lot of new relaxation methods as well as a lot of new relaxed parallel nonlinear multisplitting methods for solving the nonlinear complementarity problems the two sided approximation properties and the influences on the convergence rates from the relaxation parameters about our new methods are shown and sufficient conditions guaranteeing the methods to converge globally are discussed finally a lot of numerical results show that our new methods are feasible and efficient

general framework stability and error analysis for numerical stiff boundary value methods this paper provides a general framework called theoretical multiple shooting within which various numerical methods for stiff boundary value ordinary differential problems can be analyzed a global stability and error analysis is given allowing as much as possible the specificities of an actual numerical method to come in only locally we demonstrate the use of our results for both one sided and symmetric difference schemes the class of problems treated includes some with internal e g turning point layers

numerical inversion of laplace transform on the real line from expected values a numerical method for inversion of laplace transform f s of probability densities given for real s 0 only is proposed fractional calculus allows us to have expected values from f s or f s then the maximum entropy technique provides the analytical form of the approximant fractional moments are mainly investigated entropy and cross entropy convergence are proved some numerical tests are illustrated

convergence of best entropy estimates given a finite number of moments of an unknown density on a finite measure space the best entropy estimate that nonnegative density x with the given moments which minimizes the boltzmann shannon entropy i x x log x is considered a direct proof is given that i has the kadec property in l if yn converges weakly to 37 and i yn converges to i 37 then yn converges to 37 in norm as a corollary it is obtained that as the number of given moments increases the best entropy estimates converge in li norm to the best entropy estimate of the limiting problem which is simply in the determined case furthermore for classical moment problems on intervals with strictly positive and sufficiently smooth error bounds and uniform convergence are actually obtained

on best possible order of convergence estimates in the collocation method and galerkin s method for singularly perturbed boundary value problems for systems of first order ordinary differential equations the collocation method and galerkin method using parabolic splines are considered special adaptive meshes whose number of knots is independent of the small parameter of the problem are used unimprovable estimates in the l norm are obtained for the galerkin method these estimates are quasioptimal while for the collocation method they are suboptimal

quasi neutral limit to the drift diffusion models for semiconductors with physical contact insulating boundary conditions and the general sign changing doping profile abstract the quasi neutral limit in a bipolar drift diffusion model for semiconductors with physical contact insulating boundary conditions the general sign changing doping profile and general initial data which allow the presence of the left and right boundary layers and the initial layers is studied in the one dimensional case the dynamic structure stability of the solution with respect to the scaled debye length is proven by the asymptotic analysis of singular perturbation and the entropy energy method the key point of the proof is to use sufficiently the fact that the length of the boundary layer is very small in a short time period

a singular perturbation analysis of the fundamental semiconductor device equations in this paper we present a singular perturbation analysis of the fundamental semiconductor device equations which form a system of three second order elliptic differential equations subject to mixed neumann dirichlet boundary conditions the system consists of poisson s equation and the continuity equations and describes potential and carrier distributions in an arbitrary emiconductor device the singular perturbation parameter is the minimal normed debye length of the device under consideration using matched asymptotic expansions we demonstrate the occurrence of internal layers at surfaces across which the impurity distribution appearing as an inhomogeneity of poisson s equation has a jump discontinuity these surfaces are called junctions and the occurrence of boundary layers at semiconductor oxide interfaces we derive the layer equations and the reduced problem charge neutral approximation and give existence proofs for these problems the layer solutions which characterize the solutions of the s

new comparison theorem for the nonlinear multisplitting relaxation method for the nonlinear complementarity problems abstract a new comparison theorem on the monotone convergence rates of the parallel nonlinear multisplitting accelerated overrelaxation aor method for solving the large scale nonlinear complementarity problem is established thus the monotone convergence theory of this class of method is completed

local convergence of quasi newton methods for b differentiable equations we study local convergence of quasi newton methods for solving systems of nonlinear equations defined by b differentiable functions we extend the classical linear and superlinear convergence results for general quasi newton methods as well as for broyden s method we also show how broyden s method may be applied to nonlinear complementarity problems and illustrate its computational performance on two small examples

entropy estimate of probability densities having assigned moments stieltjes case we consider an absolutely continuous positive random variable having assigned the first algebraic moments in terms of given moments is provided an upper bound for entropy for all the distributions admitting moment generating function

on some difference schemes for singular singularly perturbed boundary value problems singularly perturbed boundary value ordinary differential problems are considered where the problem defining the reduced solution is singular for numerical approximation families of symmetric difference schemes which are equivalent to certain collocation schemes based on gauss and lobatto points are used convergence results previously obtained for the regular singularly perturbed case are extended while gauss schemes are extended with no change lobatto schemes require a small modification in the mesh selection procedure with meshes as prescribed in the text highly accurate solutions can be obtained with these schemes for singular singularly perturbed problems at a very reasonable cost this is demonstrated by examples

parallel newton methods for the nonlinear complementary problem in this paper we discuss how the basic newton method for solving the nonlinear complementarity problem can be implemented in a parallel computation environment we propose some synchronized and asynchronous newton methods and establish their convergence

maximum entropy in the finite stieltjes and hamburger moment problem a necessary and sufficient condition for the existence of the maximum entropy me function defined in an infinite or semiinfinite interval is provided the conclusions reached show that except in a few particular cases the necessary and sufficient conditions for the existence of maximum entropy function are identical to the conditions for the solution of the moment problem when the first m 1 moments are assigned even if the conclusions reached are very similar to the hausdorff case the specificity of the hamburger and stieltjes cases demands a different handling a sufficient condition for the entropy convergence of the resulting sequence of maximum entropy estimators to the entropy of the recovering function is also provided

entropy convergence in stieltjes and hamburger moment problem in the classical stieltjes and hamburger moment problem the sequence of maximum entropy approximants whose first m moments are equal to given ones is considered it is proved that whenever an infinite moment problem is determined then maximum entropy approximants converge in entropy to the function characterized by given moments entropy convergence is proved by using exclusively existence and uniqueness conditions