scholarly journals The exact solution of nonlinear operator equation AuBu+Cu=f

2006 ◽  
Vol 317 (1) ◽  
pp. 113-126
Author(s):  
Ming-gen Cui ◽  
Zhong Chen
Keyword(s):  
Exact Solution ◽  
Operator Equation ◽  
Nonlinear Operator ◽  
Nonlinear Operator Equation

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.

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.

scholarly journals Semilocal Convergence Theorem for the Inverse-Free Jarratt Method under New Hölder Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Yueqing Zhao ◽  
Rongfei Lin ◽  
Zdenek Šmarda ◽  
Yasir Khan ◽  
Jinbiao Chen ◽  
...  
Keyword(s):  
Banach Space ◽  
Error Estimate ◽  
Convergence Analysis ◽  
Operator Equation ◽  
Convergence Theorem ◽  
Nonlinear Operator ◽  
Semilocal Convergence ◽  
Nonlinear Operator Equation ◽  
Jarratt Method ◽  
Semilocal Convergence Theorem

Under the new Hölder conditions, we consider the convergence analysis of the inverse-free Jarratt method in Banach space which is used to solve the nonlinear operator equation. We establish a new semilocal convergence theorem for the inverse-free Jarratt method and present an error estimate. Finally, three examples are provided to show the application of the theorem.

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