bluuebunny/crossref_metadata_2025_split huggingface dataset:
One-leg Integration of Ordinary Differential Equations with Global Error Control
Authors: Kulikov Gennady Yu. , Shindin Sergey K. 
Published: April 2013

AbstractIn this paper we study the family of one-leg two-step second-order methods developed by Dahlquist et al., which possess the A-stability and G-stability
properties on any grid. These methods are implemented with the local-global step size control derived by Kulikov and Shindin with the aim to obtain automatically the
numerical solution with any reasonable accuracy set by the user. We show that the error control is more complicated in one-leg methods, especially when applied to stiffproblems. Thus, we adapt our local-global step size control for the methods indicated
above and test these adaptive algorithms in practice.
Finite-difference Approximation of Mathematical Physics Problems on Irregular Grids
Authors: Vabishchevich P. N. 
Published: April 2013

Abstract Mathematical physics problems are often formulated by means of the
vector analysis differential operators: divergence, gradient and rotor. For approximate
solutions of such problems it is natural to use the corresponding operator statements
for the grid problems, i.e., to use the so-called VAGO (Vector Analys Grid Operators)
method. In this paper, we discuss the possibilities of such an approach in using gen-
eral irregular grids. The vector analysis di®erence operators are constructed using
the Delaunay triangulation and the Voronoi diagrams. The truncation error and the
consistency property of the di®erence operators constructed on two types of grids are
investigated. Construction and analysis of the di®erence schemes of the VAGO method
for applied problems are illustrated by the examples of stationary and non-stationary
convection-diffusion problems. The other examples concerned the solution of the non-
stationary vector problems described by the second-order equations or the systems of
first-order equations.
Three Matlab Implementations of the Lowest-order Raviart-Thomas Mfem with a Posteriori Error Control
Authors: Bahriawati C. , Carstensen C. 
Published: April 2013

Abstract The numerical approximation of the Laplace equation with inhomogeneous mixed boundary conditions in 2D with lowest-order
Raviart-Thomas mixed finite elements is realized in three flexible and short MATLAB programs. It is the aim of this paper to derive, document, illustrate, and validate the three MATLAB implementations EBmfem, LMmfem, and CRmfem for further use and modification in education and research. A posteriori error control with a reliable and efficient averaging technique is included to monitor the discretization error. Therein, emphasis is on the correct treatment of mixed boundary conditions. Numerical examples illustrate some applications of the provided software and the quality of the error estimation.
Functional-discrete Method (FD-method) for Matrix Sturm-Liouville Problems
Authors: Bandyrskiĭ B. Ĭ. , Gavrilyuk I. P. , Lazurchak I. I. , Makarov V. L. 
Published: April 2013

AbstractA new algorithm for Sturm|Liouville problems with matrix coefficients is proposed which possesses the convergence rate of a geometric progression with a denominator depending inversely proportional on the order number of eigenvalues. The
asymptotic behavior of the distance between neighboring eigenvalues if the order number tends to infinity is investigated too. Numerical examples confirming the theoretical results are given.
Error Analysis for a Galerkin Finite Element Method Applied to a Coupled Nonlinear Degenerate System of Advection-diffusion Equations
Authors: Fadimba Koffi B. 
Published: April 2013

AbstractWe consider a standard Galerkin Method applied to both the pressure
equation and the saturation equation of a coupled nonlinear system of degenerate
advection-diffusion equations modeling a two-phase immiscible flow through porous
media. After regularizing the problem and establishing some regularity results, we
derive error estimates for a semi-discretized Galerkin Method. A decoupled nonlinear
scheme is then proposed for a fully discretized (backward in time) Galerkin Method,
and error estimates are derived for that method. We also prove the existence and
uniqueness for the nonlinear operator intervening in the backward time discretization.
Bounds of Information Expenses in Constructing Projection Methods for Solving Ill-posed Problems
Authors: Solodky Sergei G. , Lebedeva Evgeniya V. 
Published: April 2013

AbstractAn approach to constructing regularized projection methods to solve illposed
problems is proposed. This approach is based on a modification of the Galerkin
discretization scheme. It has been established that such a modification leads to a
significant reduction of information expenses compared to other known methods.
Transport-stabilized Semidiscretizations of the Incompressible Navier—Stokes Equations
Authors: Angermann L. 
Published: April 2013

AbstractWithin the framework of finite element methods, the paper investigates a
general approximation technique for the nonlinear convective term of Navier — Stokes
equations. The approach is based on an upwind method of the finite volume type. It
has been proved that the discrete convective term satisfies the well-known collection
of sufficient conditions for convergence of the finite element solution. For a particular
nonconforming scheme, the assumptions have been verified in detail and the estimate
of the semidiscrete velocity error has been proved.
Stability of Solutions of Differential-operator and Operator-difference Equations in the Sense of Perturbation of Operators
Authors: Jovanović B. S. , Lemeshevsky S. V. , Matus P. P. , Vabishchevich P. N. 
Published: April 2013

Abstract Estimates of stability in the sense perturbation of the operator for
solving first- and second-order differential-operator equations have been obtained. For
two- and three-level operator-difference schemes with weights similar estimates hold.
Using the results obtained, we construct estimates of the coefficient stability for onedimensional
parabolic and hyperbolic equations as well as for the difference schemes
approximating the corresponding differential problems.
Stability of the Difference Schemes for the Equations of Weakly Compressible Liquid
Authors: Matus P. , Korolyova O. , Chuiko M. 
Published: April 2013

Abstract A priory estimates of the stability in the sense of the initial data
of the difference scheme approximating weakly compressible liquid equations in the
Riemann invariants have been obtained. These estimates have been proved without
any assumptions about the properties of the solution of the differential problem and
depend only on the behavior of the initial conditions. As distinct from linear problems,
the obtained estimates of stability in the general case exist only for a finite instant of
time t≤t_0. In particular, this is confirmed by the fact, that nonfulfilment of these
stability conditions lead to the appearance of supersonic flows or domains with large
gradients. The questions of uniqueness and convergence of the difference solution are
considered also. The results of the computating experiment confirming the theoretical
conclusions are given.
Numerical Enclosures for Variational Inequalities
Authors: Plum M. , Wieners Ch. 
Published: April 2013

AbstractWe present a new method for proving the existence of a unique solution
of variational inequalities within guaranteed close error bounds to a numerical
approximation. The method is derived for a specific model problem featuring most
of the difficulties of perfect plasticity. We introduce a finite element method for the
computation of admissible primal and dual solutions which a posteriori guarantees the
existence of a unique solution (by the verification of the safe load condition) and which
allows determination of a guaranteed error bound. Finally, we present explicit existence
results and error bounds in some significant specific configurations.
Nonlinear Stability Of The Difference Schemes For Equations Of Isentropic Gas Dynamics
Authors: MATUS P. , KOLODYNSKA A. 
Published: April 2013

AbstractFor the difference scheme approximating the gas dynamics problem in Riemann invariants a priory estimates with respect
to the initial data have been obtained. These estimates are proved without any assumptions about the solution of the
differential problem using only limitations for the initial and boundary conditions. Estimates of stability in the general
case have been obtained only for the finite instant of time. The uniqueness and convergence
of the difference solution are also considered. The results of the numerical experiment confirming theoretical results are given.
Tomographic Approach For Tropospheric Water Vapor Detection
Authors: MIIDLA P. , RANNAT K. , UBA P. 
Published: April 2013

AbstractThe technical successes in radio navigation and the availability of nu-merical algorithms have promoted the implementation of GPS-technology to atmo-spheric sciences. The tomographical contribution of Global Satellite Navigation Sys-tems (GNSS) is possible due to the methods of high precision detection of tropospheric delays of navigation signals from satellites to receivers. The principal specific char-acter in initial constraints, data collection and assimilation methods, the obtaining of final numerical results and their interpretation make the continuation of the success story for GPS-tomography very challenging. The authors use numerical simulation as the most time- and cost-efficient way to study different processes related to tro-pospheric water vapor tomography. This paper tends to give a short overview about some known methods in GPS-tomography for detection, monitoring and modeling of the tropospheric water vapor. The possible mathematical approach to the construc-tion of virtual network of ground-based sensors (GPS-receivers) for a real geographical location and discretization of the troposphere, also some aspects of raw data filtering and analysis are described. Output of tomographical modelling of the troposphere can be used to improve the results of large-scale numerical weather prediction models and also real-time navigation. The questions of voxel geometry and methods of data processing are supposed to be the key questions in constructing an effective network of GPS-receivers for water vapor tomography.
A Defect Correction Method for the Evolutionary Convection — Diffusion Problem with Increased Time Accuracy
Authors: LABOVSKY A. 
Published: April 2013

AbstractThis work presents a defect correction
method with increased time accuracy. The desired time accuracy is attained with
no extra computational cost. The method is applied to the evolutionary transport
problem, and is proven to be unconditionally stable. In the defect step, the artificial
viscosity parameter is added to the Peclet number as a stability factor, and the system is
antidiffused in the correction step. The time accuracy is also increased in the correction
step by modifying the right hand side.Computational results verifying the claimed space
and time accuracy of the approximate solution are presented.
Numerical Solution of Systems of Singularly Perturbed Differential Equations
Authors: Linss T. , Stynes M. 
Published: April 2013

AbstractA survey is given of current research into the numerical solution of timeindependent
systems of second-order differential equations whose diffusion coefficients
are small parameters. Such problems are in general singularly perturbed. The equations
in these systems may be coupled through their reaction and/or convection terms.
Only numerical methods whose accuracy is guaranteed for all values of the diffusion
parameters are considered here. Some new unifying results are also presented.
Ultraspherical Differentiation Method for Solving System of Initial Value Differential Algebraic Equations
Authors: El-kady M. , Ibrahim M.A. 
Published: April 2013

AbstractIn this paper, we introduce a new spectral method based on ultraspherical
polynomials for solving systems of initial value differential algebraic equations.
Moreover, the suggested method is applicable for a wide range of differential equations.
The method is based on a new investigation of the ultraspherical spectral differentiation
matrix to approximate the differential expressions in equations. The produced
equations lead to algebraic systems and are converted to nonlinear programming. Numerical
examples illustrate the robustness, accuracy, and efficiency of the proposed
method.
A Macro-kinetic Hybrid Model for Traffic Flow on Road Networks
Authors: Herty M. , Moutari S. 
Published: April 2013

Abstract We have developed a new hybrid model for an heterogeneous traffic
flow, based on a coupling of the Lighthill — Whitham and Richards (LWR)
macroscopic model and the kinetic model. On the highways of a road
network, we consider the macroscopic description of the traffic flow and switch to the
kinetic model to compute the mass flux through a junction. This new model reproduces
the capacity drop phenomenon at a merge junction, for instance, without imposing any
priority rule. We present some numerical simulations in which we compare the results
of the hybrid model with those given by the fully macroscopic model. Furthermore, we
illustrate the consequences of the velocity distribution on the flow through a merging
junction.
Stability and Monotonicity of Difference Schemes for Nonlinear Scalar Conservation Laws and Multidimensional Quasi-linear Parabolic Equations
Authors: Matus P. , Lemeshevsky S. 
Published: April 2013

Abstract We have proved the difference analogue of a Bihari-type inequality.
Using this inequality, we study the stability in C and monotonicity of the difference
schemes approximating initial-boundary value problems for nonlinear conservation laws
and multi-dimensional parabolic equations. It has been shown that in the nonlinear
case the stability and monotonicity are determined not only by the behavior of the
approximate solution but also by its difference derivatives appearing in the nonlinear
terms of the equation. The stability estimates are obtained without any assumptions
about the properties of the solution and nonlinear coefficients of the differential problem.
Here we use restrictions only on input data (initial and boundary conditions and
the right-hand side).
The sufficient conditions of the shock wave generation is formulated for input data.
For the Riemann problem two exact and stable difference schemes are analyzed.
Numerical Treatments for Volterra Delay Integro-differential Equations
Authors: Rihan F. A. , Doha E. H. , Hassan M. I. , Kamel N. M. 
Published: April 2013

AbstractThis paper presents a new technique for numerical treatments of Volterra
delay integro-differential equations that have many applications in biological and physical
sciences. The technique is based on the mono-implicit Runge — Kutta method for treating the differential part and the collocation method (using
Boole’s quadrature rule) for treating the integral part. The efficiency and stability
properties of this technique have been studied. Numerical results are presented to
demonstrate the effectiveness of the methodology.
Numerical Solution of a Nonlocal Problem Modelling Ohmic Heating of Foods
Authors: Nikolopoulos C. V. 
Published: April 2013

Abstract An upwind and a Lax-Wendroff scheme are introduced for the solution
of a one-dimensional non-local problem modelling ohmic heating of foods. The schemes
are studied regarding their consistency, stability, and the rate of convergence for the
cases that the problem attains a global solution in time. A high resolution scheme is
also introduced and it is shown that it is total-variation-stable. Finally some numerical
experiments are presented in support of the theoretical results.
Adaptive Galerkin Finite Element Methods for the Wave Equation
Authors: Bangerth W. , Geiger M. , Rannacher R. 
Published: April 2013

AbstractThis paper gives an overview of adaptive discretization methods for linear
second-order hyperbolic problems such as the acoustic or the elastic wave equation.
The emphasis is on Galerkin-type methods for spatial as well as temporal discretization,
which also include variants of the Crank-Nicolson and the Newmark finite difference
schemes. The adaptive choice of space and time meshes follows the principle of \goaloriented"
adaptivity which is based on a posteriori error estimation employing the
solutions of auxiliary dual problems.
Finite Difference Method for a Second-order Ordinary Differential Equation with a Boundary Condition of the Third Kind
Authors: Pandey P.K. 
Published: April 2013

Abstract We present a second-order finite difference method for obtaining a solution of a second
order two-point boundary value problem subject to Sturm's boundary conditions. We use equidistant
discretization points, and the discretization of the differential equation at an interior point
is based on just two evaluations of the function. Numerical examples are considered and the
convergence of the proposed method is proved computationally.
Analysis of a Class of Penalty Methods for Computing Singular Minimizers
Authors: Carstensen C. , Ortner C. 
Published: April 2013

AbstractAmongst the more exciting phenomena in the field of nonlinear partial
differential equations is the Lavrentiev phenomenon which occurs in the calculus of
variations. We prove that a conforming finite element method fails if and only if the
Lavrentiev phenomenon is present. Consequently, nonstandard finite element methods
have to be designed for the detection of the Lavrentiev phenomenon in the computational
calculus of variations.
We formulate and analyze a general strategy for solving variational problems in the
presence of the Lavrentiev phenomenon based on a splitting and penalization strategy.
We establish convergence results under mild conditions on the stored energy function.
Moreover, we present practical strategies for the solution of the discretized problems
and for the choice of the penalty parameter.
Computation of the Hartree-Fock Exchange by the Tensor-Structured Methods
Authors: Khoromskaia V. 
Published: April 2013

AbstractWe propose a novel numerical method for fast and accurate evaluation
of the exchange part of the Fock operator in the Hartree-Fock equation which
is a (nonlocal) integral operator. Usually, this challenging computational
problem is solved by analytical evaluation of two-electron integrals using the “analytically
separable” Galerkin basis functions, like Gaussians. Instead, we employ the
agglomerated “grey-box” numerical computation of the corresponding six-dimensional
integrals in the tensor-structured format which does not require analytical separability
of the basis set. The point of our method is a low-rank tensor representation of arising
functions and operators on an n×n×n Cartesian grid and the implementation of the
corresponding multi-linear algebraic operations in the tensor product format. Linear
scaling of the tensor operations, including the 3D convolution product, with respect to
the one-dimension grid size n enables computations on huge 3D Cartesian grids thus
providing the required high accuracy. The presented algorithm for evaluation of the
exchange operator and a recent tensor method for the computation of the Coulomb
matrix are the main building blocks in the numerical solution of the Hartree-Fock equation
by the tensor-structured methods. These methods provide a new tool for algebraic
optimization of the Galerkin basis in the case of large molecules.
A Posteriori Error Estimates for Approximate Solutions of the Barenblatt-Biot Poroelastic Model
Authors: Nordbotten J.M. , Rahman T. , Repin S.I. , Valdman J. 
Published: April 2013

AbstractThe paper is concerned with the Barenblatt-Biot model in the theory of
poroelasticity. We derive a guaranteed estimate of the difference between exact and approximate
solutions in a combined norm that encompasses errors for the pressure fields
computed from the diffusion part of the model and errors related to stresses (strains)
of the elastic part. Estimates do not contain generic (mesh-dependent) constants and
are valid for any conforming approximation of the pressure and stress fields.
Approximate Solution of a Singular Integral Cauchy-Kernel Equation of the First Kind
Authors: Kashfi M. , Shahmorad S. 
Published: April 2013

AbstractIn this paper we present a method for the numerical solution of Cauchy
type singular integral equations of the first kind on a finite segment which is unbounded
at the end points of the segment. Chebyshev polynomials of the first and second kinds
are used to derive an approximate solution. Moreover, an estimation error is computed
for the approximate solution.
Derivative-Free Optimal Iterative Methods
Authors: Khattri S.K. , Agarwal R.P. 
Published: April 2013

AbstractIn this study, we develop an optimal family of derivative-free iterative
methods. Convergence analysis shows that the methods are fourth order convergent,
which is also verified numerically. The methods require three functional evaluations
during each iteration. Though the methods are independent of derivatives, computa-
tional results demonstrate that the family of methods are efficient and demonstrate
equal or better performance as compared with many well-known methods and the clas-
sical Newton method. Through optimization we derive an optimal value for the free
parameter and implement it adaptively, which enhances the convergence order without
increasing functional evaluations.
Quantics-TT Collocation Approximation of Parameter-Dependent and Stochastic Elliptic PDEs
Authors: Khoromskij B.N. , Oseledets I. 
Published: April 2013

Abstract
We investigate the convergence rate of the quantics-TT (QTT) stochas-
tic collocation tensor approximations to solutions of multiparametric elliptic PDEs and
construct efficient iterative methods for solving arising high-dimensional parameter-
dependent algebraic systems of equations. Such PDEs arise, for example, in the para-
metric, deterministic reformulation of elliptic PDEs with random field inputs, based,
for example, on the M-term truncated Karhunen-Loève expansion. We consider both
the case of additive and log-additive dependence on the multivariate parameter. The
local-global versions of the QTT-rank estimates for the system matrix in terms of the
parameter space dimension is proven. Similar rank bounds are observed in numerics for
the solutions of the discrete linear system. We propose QTT-truncated iteration based
on the construction of solution-adaptive preconditioner that provides robust conver-
gence in both additive and log-additive cases. Various numerical tests indicate that the
numerical complexity scales almost linearly in the dimension of parametric space M.
Feedback controls for continuous priority models in supply chain management
Authors: Herty Michael , Ringhofer Christian 
Published: April 2013

AbstractWe are interested in closed loop feedback control laws for supply chains. The mathematical
modeling is based on Boltzmann–type equations. These equations allow to model a supply chain
with priorities. The latter influence the processing time in a nonlinear way. For this class
of models we derive a control law and we show numerical results.