A Uniformly Convergent Difference Scheme for a Semilinear Singular Perturbation Problem.
A uniformly convergent quadratic spline difference scheme for singular perturbation problems
A Weyl-Titchmarsh type formula for a discrete Schrödinger operator with Wigner-von Neumann potential
We consider a discrete Schrödinger operator 𝒥 with Wigner-von Neumann potential not belonging to l². We find the asymptotics of orthonormal polynomials associated to 𝒥. We prove a Weyl-Titchmarsh type formula, which relates the spectral density of 𝒥 to a coefficient in the asymptotics of the orthonormal polynomials.
A WKB analysis of the Alfvén spectrum of the linearized magnetohydrodynamics equations
Small perturbations of an equilibrium plasma satisfy the linearized magnetohydrodynamics equations. These form a mixed elliptic-hyperbolic system that in a straight-field geometry and for a fixed time frequency may be reduced to a single scalar equation div, where may have singularities in the domaind of definition. We study the case when is a half-plane and possesses high Fourier components, analyzing the changes brought about by the singularity . We show that absorptions of energy takes...
Absolutely convergent expansions associated with a boundary-value problem with the eigenvalue parameter contained in one boundary condition
Addendum to a paper of Craig and Goodman.
Almost everywhere convergence of the inverse Jacobi transform and endpoint results for a disc multiplier
The maximal operator S⁎ for the spherical summation operator (or disc multiplier) associated with the Jacobi transform through the defining relation for a function f on ℝ is shown to be bounded from into for (4α + 4)/(2α + 3) < p ≤ 2. Moreover S⁎ is bounded from into . In particular converges almost everywhere towards f, for , whenever (4α + 4)/(2α + 3) < p ≤ 2.
Almost Periodic Solutions of Singularly Perturbed Systems of Differential Equations with Impulse Effect.
An algorithmic determination of optimal measure from data and some applications.
An Analysis and Improvement of the El~mistikawy and Werle Scheme
An elementary proof of asymptotic behavior of solutions of U" = VU
We provide an elementary proof of the asymptotic behavior of solutions of second order differential equations without successive approximation argument.
An equivalence theorem concerning population growth in a variable environment.
An existence theorem for certain solutions of algebraic differential equations in sectors
An extension of the Newton-Puiseux polygon construction to give solutions of Pfaffian forms
We give a proof of the fact that any holomorphic Pfaffian form in two variables has a convergent integral curve. The proof gives an effective method to construct the solution, and we extend it to get a Gevrey type solution for a Gevrey form.
An Improved Boundary Layer Estimate for a Singularly Perturbed Initial Value Problem.
An ODE-Solver Based on the Method of Averaging.
Analysis of singularities and of integrability of ODE's by algorithms of Power Geometry
Here we present basic ideas and algorithms of Power Geometry and give a survey of some of its applications. In Section 2, we consider one generic ordinary differential equation and demonstrate how to find asymptotic forms and asymptotic expansions of its solutions. In Section 3, we demonstrate how to find expansions of solutions to Painlevé equations by this method, and we analyze singularities of plane oscillations of a satellite on an elliptic orbit. In Section 4, we consider the problem of local...
Analytical approximation to solutions of singularly perturbed boundary value problems.
Application of uniform asymptotics to the fifth Painlevé transcendent.
Applications of the method of barriers. II: Some singularly perturbed problems.