Geometric singular perturbation theory for ordinary differential equations

Geometric singular perturbation theory for stochastic differential equations

We consider slow–fast systems of differential equations, in which both the slow and fast variables are perturbed by additive noise. When the deterministic system admits a uniformly asymptotically stable slow manifold, we show that the sample paths of the stochastic system are concentrated in a neighbourhood of the slow manifold, which we construct explicitly. Depending on the dynamics of the re...

INVESTIGATION OF BOUNDARY LAYERS IN A SINGULAR PERTURBATION PROBLEM INCLUDING A 4TH ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we investigate a singular perturbation problem including a fourth order O.D.E. with general linear boundary conditions. Firstly, we obtain the necessary conditions of solution of O.D.E. by making use of fundamental solution, then by compatibility of these conditions with boundary conditions, we determine that, for given perturbation problem, whether boundary layer is formed or not.

Geometric Singular Perturbation Theory

investigation of boundary layers in a singular perturbation problem including a 4th order ordinary differential equations

in this paper, we investigate a singular perturbation problem including a fourth order o.d.e. with general linear boundary conditions. firstly, we obtain the necessary conditions of solution of o.d.e. by making use of fundamental solution, then by compatibility of these conditions with boundary conditions, we determine that, for given perturbation problem, whether boundary layer is formed or not.

Modified Laplace Decomposition Method for Singular IVPs in the second-Order Ordinary Differential Equations

  In this paper, we use modified Laplace decomposition method to solving initial value problems (IVP) of the second order ordinary differential equations. Theproposed method can be applied to linear and nonlinearproblems