scholarly journals An Iterative Technique to Solve Fuzzy Delay Integro-Differential Equations

2021 ◽  
Author(s):  
T.L. Yookesh ◽  
T.P. Latchoumi ◽  
K.Balamurugan
Keyword(s):  
Differential Equations ◽  
Iterative Technique ◽  
System A ◽  
Differential Condition

Abstract In this exploration work, we make an assessment on the get together of nonlinear Volterra fuzzy delay integro-differential conditions, with the help of an iterative technique. The outcome is contrasted with the precise outcome with verify the legitimacy and proficiency of the method to deal with nonlinear Volterra fuzzy delay integro-differential condition. To display the suitable highlights of this proposed system, a numerical worldview is represented.

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

A Friendly Iterative Technique for Solving Nonlinear Integro-Differential and Systems of Nonlinear Integro-Differential Equations

2018 ◽  
Vol 15 (03) ◽  
pp. 1850016 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Approximate Solution ◽  
Differential Operator ◽  
Differential Equations ◽  
The Other ◽  
Iterative Technique ◽  
Restrictive Assumption ◽  
Numerical Examples ◽  
Linear And Nonlinear ◽  
Computational Procedures ◽  
Adomian’S Polynomials

In this work, a simple new iterative technique based on the integral operator, the inverse of the differential operator in the problem under consideration, is introduced to solve nonlinear integro-differential and systems of nonlinear integro-differential equations (IDEs). The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, it does not require discretization, linearization or any restrictive assumption of any form in providing analytical or approximate solution to linear and nonlinear equations. Also, this technique does not require calculating Adomian’s polynomials, Lagrange’s multiplier values or equating the terms of equal powers of the impeding parameter which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.

ON SUFFICIENT CONDITIONS OF EXPONENTIAL STABILITY FOR SYSTEMS OF LINEAR AUTONOMOUS DIFFERENTIAL EQUATIONS WITH AFTEREFFECT

2021 ◽  
Vol 28 (28) ◽  
pp. 73-83
Author(s):  
T. SABATULINA SABATULINA
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Fundamental Matrix ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Comparison System ◽  
System A ◽  
Differential Equa ◽  
Functional Differential ◽  
Autonomous Differential Equations

We consider systems of linear autonomous functional differential equa-tion with aftereffect and propose an approach to obtain effective sufficient conditions of exponential stability for these systems. In the approach we use the positiveness of the fundamental matrix of an auxiliary system (a comparison system) with concentrated and distributed delays.

scholarly journals Third-Order Neutral Delay Differential Equations: New Iterative Criteria for Oscillation

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Osama Moaaz ◽  
Emad E. Mahmoud ◽  
Wedad R. Alharbi
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Iterative Technique ◽  
Neutral Delay ◽  
Third Order ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
New Criterion ◽  
New Criteria

This study is aimed at developing new criteria of the iterative nature to test the oscillation of neutral delay differential equations of third order. First, we obtain a new criterion for the nonexistence of the so-called Kneser solutions, using an iterative technique. Further, we use several methods to obtain different criteria, so that a larger area of the models can be covered. The examples provided strongly support the importance of the new results.

Gain Scheduling-Inspired Control for Nonlinear Partial Differential Equations

2009 ◽  
Author(s):  
Antranik A. Siranosian ◽  
Miroslav Krstic ◽  
Andrey Smyshlyaev ◽  
Matt Bement
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Design Method ◽  
Nonlinear Partial Differential Equations ◽  
Gain Scheduling ◽  
System Control ◽  
Nonlinear Feedback ◽  
Partial Differential ◽  
System A ◽  
Shear Beam

We present a control design method for nonlinear partial differential equations (PDEs) based on a combination of gain scheduling and backstepping theory for linear PDEs. A benchmark first-order hyperbolic system with a destabilizing in-domain nonlinearity is considered first. For this system a nonlinear feedback law based on gain scheduling is derived explicitly, and a statement of stability is presented for the closed-loop system. Control designs are then presented for a string and shear beam PDE, both with Kelvin-Voigt damping and potentially destabilizing free-end nonlinearities. String and beam simulation results illustrate the merits of the gain scheduling approach over the linearization-based design.

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