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Solving a system of nonlinear equations with the use of optimization methods in problems related to the wheel-rail contact

Jureczko M., Duda S.

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 2

53--64

The article presents the methods for defining the geometry of the contact surface between a rigid wheel and a rigid rail. The calculation model that has been developed allowed for any arrangement of the wheel in relation to the rail. This allowed for the creation of a system of nonlinear equations, the solution of which allows one to determine the presumable wheel-rail contact points. The search for the solution of the system of strongly nonlinear equations was conducted using a few optimization methods. This allowed one to study both the selection of the starting point and the convergence of the method.

Existence, uniqueness and estimates of classical solutions to some evolutionary system

Sapa L.

Opuscula Mathematica

2015

Vol. 35, no. 6

935--956

The theorem of the local existence, uniqueness and estimates of solutions in Hölder spaces for some nonlinear differential evolutionary system with initial conditions is formulated and proved. This system is composed of one partial hyperbolic second-order equation and an ordinary subsystem with a parameter. In the proof of the theorem we use the Banach fixed-point theorem, the Arzeli-Ascola lemma and the integral form of the differential problem.