Piecewise Analytic Method

Piecewise Analytic Subactions for Analytic Dynamics

We consider a piecewise analytic expanding map f : [0, 1] → [0, 1] of degree d which preserves orientation, and an analytic positive potential g : [0, 1] → R. We address the analysis of the following problem: for a given analytic potential β log g, where β is a real constant, it is well known that there exists a real analytic (with a complex analytic extension to a small complex neighborhood of...

Polynomial operators for spectral approximation of piecewise analytic functions

We construct a sequence of globally defined polynomial valued operators, using linear combinations of either the coefficients in the orthogonal polynomial expansion of the target function with respect to a very general mass distribution μ or the values of the function at suitable points on [−1, 1], so that the degree of approximation by these operators globally is commensurate with the degree o...

Analytic Center Cutting-Plane Method

A Method of Piecewise-Smooth Numerical Branching

Analytical Approach to Differential Equations with Piecewise Continuous Arguments via Modified Piecewise Variational Iteration Method

In the present article, we apply the modified piecewise variational iteration method to obtain the approximate analytical solutions of the differential equations with piecewise continuous arguments. This technique provides a sequence of functions which converges to the exact solution of the problem. Moreover, this method reduces the volume of calculations because it does not need discretization...