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20110811BuchIterative operatorsplitting methods for nonlinear differential equations and applications of deposition processes In this article we consider iterative operatorsplitting methods for nonlinear differential equations. The main feature of the proposed idea is the embedding of Newton's method for solving the split parts of the nonlinear ...

20110920BuchIterative operatorsplitting methods for Timeirreversible Systems Theory and Application to AdvectionDiffusion EquationsIn this paper, we deduce higher order error bounds for iterative operator splitting methods for timeirreversible systems of linear advectiondiffusion equations. involving timeirreversible diffusion and a reversible ...

20110811BuchIterative operatorsplitting methods for wave equations with stability results and numerical examples We are motivated by simulating a threedimensional wave equation for an anisotropic material with stressfree boundary conditions. The applications are suited in the earthquake simulation that is based on seismic model ...

20060101BuchIterative OperatorSplitting Methods with higher order TimeIntegration Methods and Applications for Parabolic Partial Differential Equations In this paper we design higher order time integrators for systems of stiff ordinary differential equations. We could combine implicit RungeKutta and BDFmethods with iterative operatorsplitting methods to obtain higher ...

20110920BuchIterative operatorsplitting with time overlapping algorithms Theory and Application to constant and timedependent wave equationsIn this article we consider wave equations with constant and linear time dependent diffusioncoefficients which are solved numerically by iterative operator splitting with interval overlapping algorithms. The benefits of ...

20011012BuchJacobi theta embedding of a hyperbolic 4space with cusps Starting from a fixed elliptic curve with complex multiplication we compose lifted quotients of elliptic Jacobi theta functions to abelian functions in higher dimension. In some cases, where complete PicardEinstein metrics ...

20110920BuchKinetic processes and Phasetransition of CVD processes for Ti₃SiC₂ In this paper we present a kinetic model based on numerical simulations of a chemical vapor deposition (CVD) process. We discuss a model that is based on kinetics of the deposition rates to the material. Such a simple ...

20060920BuchLaGO  a (heuristic) Branch and Cut algorithm fornonconvex MINLPs We present a Branch and Cut algorithm of the software package LaGO to solve nonconvex mixedinteger nonlinear programs. A linear outer approximation is constructed from a convex relaxation of the problem. Since we do not ...

20020531BuchLagrangian Decomposition of MixedInteger AllQuadratic Programs The purpose of this paper is threefold. First we show that the Lagrangian dual of a blockseparable mixedinteger allquadratic program (MIQQP) can be formulated as an eigenvalue optimization problem keeping the blockseparable ...

20020528BuchLagrangian Smoothing Heuristics for MaxCut This paper presents smoothing heuristics for an NPhard combinatorial problem based on Lagrangian relaxation. We formulate the Lagrangian dual for this nonconvex quadratic problem and propose eigenvalue nonsmooth unconstrained ...

20051107BuchLarge time asymptotics of solutions to the anharmonic oscillator model from nonlinear optics The anharmonic oscillator model describing the propagation of electromagnetic waves in an exterior domain containing a nonlinear dielectric medium is investigated. The system under consideration consists of a generally ...

20051107BuchLevel Zero Types and Hecke Algebras for Local Central Simple Algebras Let D be a central division algebra and Ax = GLm(D) the unit group of a central simple algebra over a padic field F. The purpose of this paper is to give types (in the sense of Bushnell and Kutzko) for all level zero ...

20030915BuchLinear boundary value problems for differential algebraic equations By the use of the corresponding shift matrix, the paper gives a criterion for the unique solvability of linear boundary value problems posed for linear differential algebraic equations up to index 2 with wellmatched leading ...

20051109BuchLinear differential algebraic equations of index 1 and their adjoint equations For linear differential algebraic equations of tractability index 1 the notion of the adjoint equation is analysed in full detail. Its solvability is shown at the lowest possible smoothness. The fundamental matrices of ...

20110713BuchLinear differentialalgebraic equations with properly stated leading term Bcritical pointsWe examine in this paper socalled Bcritical points of linear, timevarying differentialalgebraic equations (DAEs) of the form A(t)(D(t)x(t))' + B(t)x(t) = q(t). These critical or singular points, which cannot be handled ...

20051103BuchLinear index1 DAEs: regular and singular problems Several features and interrelations of projector methods and reduction techniques for the analysis of linear timevarying differentialalgebraic equations (DAEs) are addressed in this work. The application of both methodologies ...

19951025BuchLinear spaces for index 2 differentialalgebraic equations In this paper we consider solution spaces of linear index2tractable differential algebraic equations. Relations between the solutions of the adjoint equations and the corresponding solution spaces are derived and, thus, ...

20040701BuchLineare Algebra individuell AufgabensammlungDiese Aufgabensammlung zur linearen Algebra ist der fachliche Teil des Schlussberichts zum BMBFProjekt 01NM075D zur interaktiven Mathematik und Informatikgrundausbildung an der HumboldtUniversität zu Berlin. Sie beinhaltet ...

20051117BuchLocal error control for general index1 and index2 differentialalgebraic equations This paper presents an error test function usable for the local error control and the automatic stepsize selection in the numerical integration of general index1 and index2 differentialalgebraic equations (DAEs). This ...

20060101BuchLocal Error Estimates for Moderately Smooth ODEs and DAEs We discuss an error estimation procedure for the local errors of low order methods applied to solve initial value problems in ordinary differential equations (ODEs) and index 1 differentialalgebraic equations (DAEs). The ...