Difference methods for problems with different time scales

Difference Methods for Problems With Different Time Scales

We consider the use of difference methods for weakly nonlinear systems of ordinary differential equations with rapidly oscillating solutions and develop a general approach which depends only on the smoothness of the coefficients and the nonlinearities. In particular, one is led to a strategy which is suitable for the detection and resolution of turning points in such systems. A computational ex...

Variational Methods for Two Resonant Problems on Time Scales∗

Using variational methods we study the generalization of two classical second order periodic problems in the context of time scales. On the one hand, we study a forced pendulum-type equation. On the other hand, we obtain solutions for a bounded nonlinearity under Landesman–Lazer type conditions. AMS subject classification: 39A12, 39A99.

Existence of solutions of boundary value problems for Caputo fractional differential equations on time scales

‎In this paper‎, ‎we study the boundary-value problem of fractional‎ ‎order dynamic equations on time scales‎, ‎$$‎ ‎^c{Delta}^{alpha}u(t)=f(t,u(t)),;;tin‎ ‎[0,1]_{mathbb{T}^{kappa^{2}}}:=J,;;1

On Stabilized Finite Element Methods for Transient Problems with Varying Time Scales

Many engineering and scientific applications require a detailed analysis of strongly coupled continuum transport and chemical reaction physics. These systems are characterized by the co-existence of advection and diffusion time scales similar to those occurring in typical flow problems, with very short time scales for non-equilibrium chemical reactions. Accurate resolution of the reaction phase...

Hyperbolic Systems with Different Time Scales