scholarly journals An iterative method for solution of nonlinear operator equation

2016 ◽  
Vol 13 (1) ◽  
pp. 6-10
Author(s):  
Nguyễn Bường
Keyword(s):  
Hilbert Space ◽  
Iterative Method ◽  
Integral Equations ◽  
Operator Equation ◽  
Iterative Process ◽  
Nonlinear Operator ◽  
Nonlinear Operator Equation ◽  
Nonlinear Integral Equations

In the note, for finding a solution of nonlinear operator equation of Hammerstein’s type an iterative process in infinite-dimentional Hilbert space is shown, where a new iteration is constructed basing on two last steps. An example in the theory of nonlinear integral equations is given for illustration.

scholarly journals OPTIMAL CONTROL FOR SYSTEMS GOVERNED BY DISCONTINUOUS NONLINEARITY

1999 ◽  
Vol 30 (4) ◽  
pp. 289-294
Author(s):  
NGUYEN BUONG
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Theoretical Result ◽  
Control Problem ◽  
Existence Theorem ◽  
Integral Equations ◽  
Operator Equation ◽  
Nonlinear Operator ◽  
Discontinuous Nonlinearity ◽  
Nonlinear Integral Equations

The aim of this paper is to present an existence theorem of optimal control for systems descrided by the operator equation of Hammerstein type $x + K F(u, x) = 0$ with the discontinuous monotone nonlinear operator $F$ in $x$. Then, the theoretical result is applied to investigate an optimal control problem for system, where the state is written in the form of nonlinear integral equations in $L_p(\omega)$.

scholarly journals SOLUTION OF A NONLINEAR OPERATOR EQUATION OF THE FIRST KIND WITH A CONTINUOUS POSITIVE LINEAR OPERATOR

2021 ◽  
pp. 118-123
Author(s):  
I.A. Usenov ◽  
R.K. Usenova ◽  
A. Nurkalieva
Keyword(s):  
Hilbert Space ◽  
Exact Solution ◽  
Approximate Solution ◽  
Linear Operator ◽  
Operator Equation ◽  
Nonlinear Operator ◽  
Regularization Parameter ◽  
Positive Linear Operator ◽  
Nonlinear Operator Equation ◽  
The Right

In the space H, a nonlinear operator equation of the first kind is studied, when the linear, nonlinear operator and the right-hand side of the equation are given approximately. Based on the method of Lavrent'ev M.M. an approximate solution of the equation in Hilbert space is constructed. The dependence of the regularization parameter on errors was selected. The rate of convergence of the approximate solution to the exact solution of the original equation is obtained.

scholarly journals On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Hameed Husam Hameed ◽  
Z. K. Eshkuvatov ◽  
Anvarjon Ahmedov ◽  
N. M. A. Nik Long
Keyword(s):  
Approximate Solution ◽  
Integral Equations ◽  
Operator Equation ◽  
Unknown Function ◽  
Existence And Uniqueness ◽  
Nonlinear Operator ◽  
Volterra Integral Equations ◽  
Nonlinear Operator Equation ◽  
Kantorovich Method ◽  
Majorant Function

We develop the Newton-Kantorovich method to solve the system of2×2nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method.

Oscillation analysis of numerical solution of Nonlinear Operator Equation

2021 ◽  
Vol 7 (5) ◽  
pp. 2111-2126
Author(s):  
Yang Zhou ◽  
Cuimei Li
Keyword(s):  
Numerical Solution ◽  
Operator Equation ◽  
Vibration Analysis ◽  
Nonlinear Operator ◽  
Vibration Spectrum ◽  
Nonlinear Operator Equation ◽  
Analysis Method ◽  
Analysis Model ◽  
Oscillation Analysis ◽  
Analysis Equation

There is a problem of low accuracy in the analysis of the vibration of the numerical solution of the nonlinear operator equation. In this work, the vibration analysis equation is constructed by the step-by-step search method, and the vibration quadrant of the equation is divided by the dichotomy method. The vibration spectrum is determined by the iteration method, and the vibration analysis model of the numerical solution of the nonlinear operator equation is constructed. The vibration analysis of the numerical solution of the nonlinear operator equation is completed based on the solution of the model and the numerical calculation and display of the step-by-step Fourier. The experimental results show that the proposed method has higher accuracy than the traditional vibration analysis method, which meets the requirements of the vibration analysis of the numerical solution of nonlinear operator equation.

scholarly journals TEMPERATURE MODELLING WITHIN A THIN MATERIAL SHEET INVOLVED IN CONDUCTIVE‐RADIATIVE HEAT TRANSFER

2005 ◽  
Vol 10 (2) ◽  
pp. 141-154
Author(s):  
K. Birgelis
Keyword(s):  
Heat Transfer ◽  
Operator Equation ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Nonlinear Operator ◽  
Nonlinear Operator Equation

In this paper we consider a problem about finding of temperature approximation within a thin material sheet involved in conductive‐radiative heat transfer. As result, we found that temperature within the sheet can be approximated in L 2 norm by solution of a simple nonlinear operator equation. Straipsnyje modeliuojamas temperatūros pasiskirstymas tarp plonu medžiagos lakštu atsižvelgiant i radiacijai laidžios šlumos pernešima. Nustatyta, kad temperatūra tarp lakštu gali būti aproksimuojama L 2 normoje paprastos netiesines operatorines lygties sprendiniais.

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