0000000000240120
AUTHOR
Melitta Fiebig-wittmaack
On the number of solutions of a Duffing equation
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.
Tridiagonal preconditioning for Poisson-like difference equations with flat grids: Application to incompressible atmospheric flow
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 …
Stability of stationary solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions
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)