0000000000240120

AUTHOR

Melitta Fiebig-wittmaack

showing 3 related works from this author

On the number of solutions of a Duffing equation

1991

The exact number of solutions of a Duffing equation with small forcing term and homogeneous Neumann boundary conditions is given. Several bifurcation diagrams are shown.

Applied MathematicsGeneral MathematicsMathematical analysisGeneral Physics and AstronomyDuffing equationBifurcation diagramNonlinear Sciences::Chaotic DynamicsBifurcation theoryNeumann boundary conditionInitial value problemCalculus of variationsBoundary value problemNonlinear Sciences::Pattern Formation and SolitonsBifurcationMathematicsZAMP Zeitschrift f�r angewandte Mathematik und Physik
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Tridiagonal preconditioning for Poisson-like difference equations with flat grids: Application to incompressible atmospheric flow

2011

AbstractThe convergence of many iterative procedures, in particular that of the conjugate gradient method, strongly depends on the condition number of the linear system to be solved. In cases with a large condition number, therefore, preconditioning is often used to transform the system into an equivalent one, with a smaller condition number and therefore faster convergence. For Poisson-like difference equations with flat grids, the vertical part of the difference operator is dominant and tridiagonal and can be used for preconditioning. Such a procedure has been applied to incompressible atmospheric flows to preserve incompressibility, where a system of Poisson-like difference equations is …

Poisson-like equationBiconjugate gradient method010504 meteorology & atmospheric sciencesTridiagonal matrixOperator (physics)Applied MathematicsLinear systemGeometryPreconditioning010103 numerical & computational mathematics01 natural sciencesComputational MathematicsConjugate gradient methodConvergence (routing)Convergence accelerationApplied mathematicsDynamic pressure0101 mathematicsCondition numberCondition numberAtmospheric model0105 earth and related environmental sciencesMathematicsFlat gridsJournal of Computational and Applied Mathematics
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Stability of stationary solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions

1991

for some x in [0, rr]. The guiding idea of this paper is to observe the changes in the stability behavior of the solutions if we perturb the autonomous problem intro- ducing a forcing term g. In [8] it was shown that iff and g are related by a boundedness condi- tion (see condition (* ) in Theorem 3.1) then there exists a stable solution of (1.1) “close” to each stable solution of (1.2). We want to call these stable solutions of (1.1)

Forcing (recursion theory)HomogeneousApplied MathematicsMathematical analysisNeumann boundary conditionStability (probability)AnalysisTerm (time)MathematicsJournal of Differential Equations
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