Enclosure Methods for Linear and Nonlinear Systems of Fredholm Integral Equations of the Second Kind

1993 ◽  
pp. 255-282 ◽  
Author(s):  
Wolfram Klein
Keyword(s):  
Nonlinear Systems ◽  
Integral Equations ◽  
Fredholm Integral Equations ◽  
Enclosure Methods ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

scholarly journals Optimal Homotopy Asymptotic and Multistage Optimal Homotopy Asymptotic Methods for Solving System of Volterra Integral Equations of the Second Kind

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Jafar Biazar ◽  
Roya Montazeri
Keyword(s):  
Nonlinear Systems ◽  
Integral Equations ◽  
Asymptotic Method ◽  
Asymptotic Methods ◽  
Volterra Integral Equations ◽  
Optimal Homotopy Asymptotic Method ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

In this paper, optimal homotopy asymptotic method (OHAM) and its implementation on subinterval, called multistage optimal homotopy asymptotic method (MOHAM), are presented for solving linear and nonlinear systems of Volterra integral equations of the second kind. To illustrate these approaches two examples are presented. The results confirm the efficiency and ability of these methods for such equations. The results will be compared to find out which method is more accurate. Advantages of applying MOHAM are also illustrated.

Mathematical modeling of conversion of non-Gaussian random processes, signals and noise in linear and nonlinear systems

2018 ◽  
pp. 66-78
Author(s):  
V. M. Artyushenko ◽  
V. I. Volovach
Keyword(s):  
Mathematical Modeling ◽  
Nonlinear Systems ◽  
Random Processes ◽  
Mathematical Transformation ◽  
Positive And Negative Feedback ◽  
Non Linear Systems ◽  
Linear And Nonlinear ◽  
Non Gaussian ◽  
Linear And Nonlinear Systems ◽  
Inertial Systems

The questions connected with mathematical modeling of transformation of non-Gaussian random processes, signals and noise in linear and nonlinear systems are considered and analyzed. The mathematical transformation of random processes in linear inertial systems consisting of both series and parallel connected links, as well as positive and negative feedback is analyzed. The mathematical transformation of random processes with polygamous density of probability distribution during their passage through such systems is considered. Nonlinear inertial and non-linear systems are analyzed.

scholarly journals New Explicit Bounds on Gamidov Type Integral Inequalities for Functions in Two Variables and Their Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Kelong Cheng ◽  
Chunxiang Guo
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Integral Inequalities ◽  
Fredholm Integral Equations ◽  
Uniqueness Of Solutions ◽  
Fredholm Type ◽  
Type Integral ◽  
Explicit Bounds ◽  
Linear And Nonlinear

Some linear and nonlinear Gamidov type integral inequalities in two variables are established, which can give the explicit bounds on the solutions to a class of Volterra-Fredholm integral equations. Some examples of application are presented to show boundedness and uniqueness of solutions of a Volterra-Fredholm type integral equation.

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