scholarly journals Set-Invariance-based Interpretations for the L1 Performance of Nonlinear Systems

2021 ◽  
Author(s):  
Hyung Tae Choi ◽  
Jung Hoon Kim
Keyword(s):  
Performance Analysis ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Invariant Set ◽  
Sufficient Condition ◽  
Analysis Problem ◽  
Invariance Principles ◽  
Set Invariance ◽  
Piecewise Continuous

Abstract This paper is concerend with tackling the L 1 performance analysis problem of continuous and piecewise continuous nonlinear systems with non-unique solutions by using the involved arguments of set-invariance principles. More precisely, this paper derives a sufficient condition for the L 1 performance of continuous nonlinear systems in terms of the invariant set. However, because this sufficient condition intrinsically involves analytical representations of solutions of the differential equations corresponding to the nonlinear systems, this paper also establishes another sufficient condition for the L 1 performance by introducing the so-called extended invariance domain, in which it is not required to directly solving the nonlinear differential equations. These arguments associated with the L 1 performance analysis is further extended to the case of piecewise continuous nonlinear systems, and we obtain parallel results based on the set-invariance principles used for the continuous nonolinear systems. Finally, numerical examples are provided to demonstrate the effectiveness as well as the applicability of the overall results derived in this paper.

scholarly journals Study of an implicit type coupled system of fractional differential equations by means of topological degree theory

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Sarwar ◽  
Anwar Ali ◽  
Mian Bahadur Zada ◽  
Hijaz Ahmad ◽  
Taher A. Nofal
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Topological Degree ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Degree Theory ◽  
Coupled System ◽  
Sufficient Condition ◽  
Topological Degree Theory ◽  
Fractional Differential

AbstractIn this work, a sufficient condition required for the presence of positive solutions to a coupled system of fractional nonlinear differential equations of implicit type is studied. To study sufficient conditions essential for the existence of unique solution degree theory is used. Two examples are given to illustrate the established results.

scholarly journals On the Method of Inverse Mapping for Solutions of Coupled Systems of Nonlinear Differential Equations Arising in Nanofluid Flow, Heat and Mass Transfer

2018 ◽  
Vol 3 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Mangalagama Dewasurendra ◽  
Kuppalapalle Vajravelu
Keyword(s):  
Mass Transfer ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Mapping Method ◽  
Coupled Systems ◽  
Inverse Mapping ◽  
Science And Engineering ◽  
Nanofluid Flow ◽  
Flow Heat

AbstractVery recently, Liao has invented a Directly Defining Inverse Mapping Method (MDDiM) for nonlinear differential equations. Liao’s method is novel and can be used for solving several problems arising in science and engineering, if we can extend it to nonlinear systems. Hence, in this paper, we extend Liao’s method to nonlinear-coupled systems of three differential equations. Our extension is not limited to single, double or triple equations, but can be applied to systems of any number of equations.

scholarly journals Piecewise continuous approach to nonlinear differential equations approximation problem of computational structural mechanics

2018 ◽  
Vol 251 ◽  
pp. 04024
Author(s):  
Roman Leibov
Keyword(s):  
Differential Equations ◽  
Random Search ◽  
Piecewise Linear ◽  
Nonlinear Differential Equations ◽  
Piecewise Linear Approximation ◽  
Continuous Approximation ◽  
Algebraic Equations ◽  
Computational Structural Mechanics ◽  
Piecewise Continuous ◽  
Linear Differential

This paper presents a nonlinear differential equations system piecewise continuous approximation. The piecewise continuous approximation improves piecewise linear approximation through reducing the errors at the boundaries of different linear differential equations systems areas. The matrices of piecewise continuous differential and algebraic equations systems are estimated using nonlinear differential equations system time responses and random search method. The results of proposed approach application are presented.

scholarly journals Characteristic Cauchy’s problem with prehistory in the case of nonlinear differential equations in partial derivatives

2020 ◽  
pp. 28-33
Author(s):  
O. I. Kohutych ◽  
V. V. Marynets
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Nonlinear Problems ◽  
Hot Water ◽  
Constructive Method ◽  
Sufficient Condition ◽  
Output Data ◽  
Partial Derivatives ◽  
Process Gas

We have built a constructive method of investigation and approximate solution for nonlinear Gursa’s problem with prehistory. We have established sufficient condition of subsistence, existence of unity and constant signs solution of the investigated problem. At mathematical description to different nature process (gas sorption, the spread of moisture in the porous substances, pipes heating by a stream of hot water, drying by the airflow, etc. [1]) we often come to boundary value problems for nonlinear differential equations in partial derivatives, when not all output data are known, that is some of them need to be found from auxiliary nonlinear problems, which are mathematical models of processes that proceeded the research. These problems should be named as problems with prehistory. One approach to investigation and approximate solution to such a problem has been proposed in the current paper.

scholarly journals Stability of Nonlinear Systems of Fractional Order Differential Equations

2010 ◽  
Vol 7 (4) ◽  
pp. 1458-1461
Author(s):  
Baghdad Science Journal
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Fractional Order ◽  
Finite Time ◽  
Time Interval ◽  
Sufficient Condition ◽  
Finite Time Interval ◽  
Infinite Time ◽  
Fractional Order Differential Equations ◽  
Infinite Time Interval

In this paper, a sufficient condition for stability of a system of nonlinear multi-fractional order differential equations on a finite time interval with an illustrative example, has been presented to demonstrate our result. Also, an idea to extend our result on such system on an infinite time interval is suggested.

scholarly journals On New Solutions of System of Shallow Water Wave Equations

2019 ◽  
Vol 7 (6) ◽  
Author(s):  
Ziad Salem Rached
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Shallow Water ◽  
Analytical Solutions ◽  
Water Wave ◽  
Wave Equations ◽  
Nonlinear Differential Equations ◽  
Shallow Water Wave ◽  
Shallow Water Wave Equations ◽  
Modified Simple Equation Method

Obtaining analytical solutions of nonlinear differential equations and nonlinear systems of partial and ordinary differential equations is an important topic in various fields of Mathematics. Many techniques are available in the literature. In this note, the enhanced modified simple equation method (EMSEM) is applied to system of shallow water wave equations.

Sign in / Sign up

Export Citation Format

Share Document