Estimation of Turning Point Location of Convex Solutions for Nonlinear Second-Order Differential Equations

Abstract

In this paper, we study the existence and location of turning points of the convex solutions for a certain class of the ordinary differential equations subject to the Dirichlet boundary conditions. We propose a practical and effective method for calculating the lower and upper bounds of turning point location.

Turning point analysis of the concave steady-state solutions for nonlinear singularly perturbed heat transfer equation

“…In this section we state a theorem which is the main result of article concerning the estimate of location of a turning point x T P, of solution y of the problem (1), (2). Theorem 4.1 (compare with [6]). Let the assumptions of Theorem 3.1 are fulfilled and let there exist Riemann integrable functions g L and g U over [a, b]…”

“…compare with[6]). The point x T P, ∈ (a, b) is a turning point of the solution y of the problem(1),(2) if and only if the integral identity(b − a) x T P, a f (s, y (s)) ds = (B − A ) + b a f (s, y (s)) (b − s)ds(3) holds.…”

Design of effective numerical scheme for solving systems with high-speed feedback

“…Physical quantities, numerically characterizing these elements enter into the model as parameters [1], [2]. [3], [4].…”