Search results for "Linear system"

Efficient computation of stable bifurcating branches of nonlinear eigenvalue problems

1983

Ober Ein Rayleigh-Ritz-Verfahren zur Bestimmung Kritischer Werte

1980

This paper is concerned with the existence of critical points for a functional f defined on the level set of a second functional g. Existence of nontrivial solutions for the nonlinear eigenvalue-problem f′(u) = λg′(u) and convergence for a nonlinear analogue to the Rayleigh-Ritz-Method is proven. The results are applied to a nonlinear ordinary eigenvalue problem where it is shown that the lowest point in the continuous spectrum of the associated linearized operator is a bifurcation point of infinite multiplicity.

Modelling and Simulation of the Longterm Behaviour of Arterial Pressure Regulation with the Aid of a Block — Diagrammed Interactive Simulation System

1983

The possibility of developing a managable closed nonlinear mathematical model of the renovascular system for longterm blood pressure regulation is outlined. The developed model is a parametric one. Its structure contains explicitely the biological parameters.

Calculation of nonlinear stationary magnetic field

1996

Currently, linear models of various physical fields can successfully be implemented numerically. Efficient numerical methods have been developed during last two or three decades and sufficiently capable computers are available. The situation is different with nonlinear models. There is no general numerical method for solving all nonlinear problems, and consequently every class of problems has to be investigated individually. The specific features of the class are taken into account in this process [Berger].

An Interactive Multiple Objective Linear Programming Method for a Class of Underlying Nonlinear Utility Functions

1983

This paper develops a method for interactive multiple objective linear programming assuming an unknown pseudo concave utility function satisfying certain general properties. The method is an extension of our earlier method published in this journal (Zionts, S., Wallenius, J. 1976. An interactive programming method for solving the multiple criteria problem. Management Sci. 22 (6) 652–663.). Various technical problems present in predecessor versions have been resolved. In addition to presenting the supporting theory and algorithm, we discuss certain options in implementation and summarize our practical experience with several versions of the method.

The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS

2002

In this paper I propose a method for solving in closed form a general class of four-dimension non-linear modified Hamiltonian dynamic systems. This method may be used to study several intertemporal optimization problems with a predetermined structure, involving unbounded technological constraints as well as multiple controls and state variables. The method is developed here by solving the first order conditions corresponding to the socially optimal solution to the Lucas (1988) two-sector model of endogenous growth.

Homoclinic Solutions of Nonlinear Laplacian Difference Equations Without Ambrosetti-Rabinowitz Condition

2021

The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using Ambrosetti-Rabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.

THE MAXWELL–DIRAC EQUATIONS: ASYMPTOTIC COMPLETENESS AND THE INFRARED PROBLEM

1994

In this article we present an announcement of results concerning: a) A solution to the Cauchy problem for the M-D equations, namely global existence, for small initial data at t = 0, of solutions for the M-D equations. b) Arguments from which asymptotic completeness for the M-D equations follows. c) Cohomological interpretation of the results in the spirit of nonlinear representation theory and its connection to the infrared tail of the electron in M-D classical field theory. The full detailed results will be published elsewhere.

Efficiency and Stability of a Family of Iterative Schemes for Solving Nonlinear Equations

2019

In this paper, we construct a family of iterative methods with memory from one without memory, analyzing their convergence and stability. The main aim of this manuscript yields in the advantage that the use of real multidimensional dynamics gives us to decide among the different classes designed and, afterwards, to select its most stable members. Some numerical tests confirm the theoretical results.

Overview of Other Results and Open Problems

2014

This chapter presents an overview of results related to error control methods, which were not considered in previous chapters. In the first part, we discuss possible extensions of the theory exposed in Chaps. 3 and 4 to nonconforming approximations and certain classes of nonlinear problems. Also, we shortly discuss some results related to explicit evaluation of modeling errors. The remaining part of the chapter is devoted to a posteriori estimates of errors in iteration methods. Certainly, the overview is not complete. A posteriori error estimation methods are far from having been fully explored and this subject contains many unsolved problems and open questions, some of which we formulate …