English
Related papers

Related papers: The homotopy analysis method and the Lienard equat…

200 papers

This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working…

Analysis of PDEs · Mathematics 2016-03-15 Khoa Vo , Adrian Muntean

The study of homotopy theoretic phenomena in the language of type theory is sometimes loosely called `synthetic homotopy theory'. Homotopy theory in type theory is only one of the many aspects of homotopy type theory, which also includes…

Logic · Mathematics 2019-06-25 Egbert Rijke

A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates…

Computational Engineering, Finance, and Science · Computer Science 2021-01-01 Alwin Förster , Malte Krack

We present an algorithm for constructing numerical solutions to one--dimensional nonlinear, variable coefficient boundary value problems. This scheme is based upon applying the Homotopy Analysis Method (HAM) to decompose a nonlinear…

Numerical Analysis · Mathematics 2019-03-27 Andrew C. Cullen , Simon R. Clarke

Analysis of the generalized Weierstrass-Enneper system includes the estimation of the degree of indeterminancy of the general analytic solution and the discussion of the boundary value problem. Several different procedures for constructing…

Analysis of PDEs · Mathematics 2015-06-26 Paul Bracken , Alfred M. Grundland

A new non-perturbative method of solution of the nonlinear Heisenberg equations in the finite-dimensional subspace is illustrated. The method, being a counterpart of the traditional Schrodinger picture method, is based on a finite operator…

Quantum Physics · Physics 2016-09-08 L. Mista , R. Filip

We consider the harmonic balance method for finding approximate periodic solutions of the Lorenz system. When developing software that implements the described method, the math package Maxima was chosen. The drawbacks of symbolic…

Dynamical Systems · Mathematics 2019-08-26 Alexander N. Pchelintsev , Andrey A. Polunovskiy , Irina Yu. Yukhanova

By a numerical continuation method called a diagonal homotopy we can compute the intersection of two positive dimensional solution sets of polynomial systems. This paper proposes to use this diagonal homotopy as the key step in a procedure…

Numerical Analysis · Mathematics 2007-05-23 Andrew J. Sommese , Jan Verschelde , Charles W. Wampler

Stochastic-periodic homogenization is studied for the Maxwell equations with nonlinear and periodic electric conductivity. It is shown by the stochastic-two-scale convergence method that the sequence of solutions of a class of highly…

Analysis of PDEs · Mathematics 2023-12-27 Joel Fotso Tachago , Hubert Nnang

In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…

Optimization and Control · Mathematics 2016-10-14 James Schmidt

The article gives an overview of the parameter numerical continuation methodology applied to setpoint control and parameter identification of nonlinear systems. The control problems for affine systems as well as general (nonaffine)…

Optimization and Control · Mathematics 2013-01-29 Alex Borisevich

In this paper we consider some non-stationary relaxed synchronous and asynchronous multi-splitting methods for solving the linear complementarity problems with their coefficient matrices being H-matrices. The convergence theorems of the…

Numerical Analysis · Mathematics 2018-03-08 Cuiyu Liu , Chenliang Li

We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…

Numerical Analysis · Mathematics 2015-06-23 James Bremer

The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…

Classical Analysis and ODEs · Mathematics 2025-01-09 Alberto Lastra

We Prove That The Uniform Upper Bound for the Number Of Limit Cycles Of The Lienard Equation of Degree 4 Can be equals to 2. Further We Suggest to Embedding Planar Lienard Equations In Higher Dimension and Present question of completly…

Classical Analysis and ODEs · Mathematics 2011-02-01 Ali Taghavi

Homotopy optimization is a traditional method to deal with a complicated optimization problem by solving a sequence of easy-to-hard surrogate subproblems. However, this method can be very sensitive to the continuation schedule design and…

Machine Learning · Computer Science 2023-07-25 Xi Lin , Zhiyuan Yang , Xiaoyuan Zhang , Qingfu Zhang

In this article we study homotopes of finite-dimensional algebras (not necessarily, associative). In the case of associative algebras we study homotopes by methods of Category theory and give description of so-called well-tempered elements…

Rings and Algebras · Mathematics 2020-05-05 Ilya Zhdanovskiy

This paper is concerned with an alternative analytical solution of time-fractional nonlinear Schrodinger equation and nonlinear coupled Schrodinger equation obtained by employing fractional reduced differential transform method. The…

Numerical Analysis · Mathematics 2016-11-23 Brajesh Kumar Singh , Pramod Kumar

We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…

Numerical Analysis · Mathematics 2020-03-31 S. Armstrong , A. Hannukainen , T. Kuusi , J. -C. Mourrat

A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the…

Classical Analysis and ODEs · Mathematics 2019-11-21 Elena Braverman , Karel Hasik , Anatoli F. Ivanov , Sergei Trofimchuk