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A new Taylor type formula and C extensions for asymptotically developable functions

M. Zurro (1997)

Studia Mathematica

The paper studies the relation between asymptotically developable functions in several complex variables and their extensions as functions of real variables. A new Taylor type formula with integral remainder in several variables is an essential tool. We prove that strongly asymptotically developable functions defined on polysectors have C extensions from any subpolysector; the Gevrey case is included.

A note on eigenvalues of ordinary differential operators.

Alan Ho (1997)

Revista Matemática Iberoamericana

In this follow-up on the work of Fefferman-Seco [FS] an improved condition for the discrete eigenvalues of the operator -d2 / dx2 + V(x) is established for V(x) satisfying certain hypotheses. The eigenvalue condition in [FS] establishes eigenvalues of this operator to within a small error. Through an obervation due to C. Fefferman, the order of accuracy can be improved if a certain condition is true. This paper improves on the result obtained in [FS] by showing that this condition does indeed hold....

A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems

Josef Dalík (1991)

Applications of Mathematics

A general construction of test functions in the Petrov-Galerkin method is described. Using this construction; algorithms for an approximate solution of the Dirichlet problem for the differential equation - ϵ u n + p u ' + q u = f are presented and analyzed theoretically. The positive number ϵ is supposed to be much less than the discretization step and the values of p , q . An algorithm for the corresponding two-dimensional problem is also suggested and results of numerical tests are introduced.

A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.

Peter Smith (1990)

Revista Matemática de la Universidad Complutense de Madrid

Saddle connections and subharmonics are investigated for a class of forced second order differential equations which have a fixed saddle point. In these equations, which have linear damping and a nonlinear restoring term, the amplitude of the forcing term depends on displacement in the system. Saddle connections are significant in nonlinear systems since their appearance signals a homoclinic bifurcation. The approach uses a singular perturbation method which has a fairly broad application to saddle...

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