scholarly journals THREE CLASSIFICATIONS ON BRANCHING PROCESSES AND THEIR BEHAVIOR FOR FINDING THE SOLUTION OF NONLINEAR INTEGRAL EQUATIONS

2010 ◽  
Vol 15 (3) ◽  
pp. 371-381
Author(s):  
Behrouz Fathi Vajargah ◽  
Mojtaba Moradi
Keyword(s):  
Integral Equation ◽  
Monte Carlo ◽  
Fixed Point ◽  
Monte Carlo Method ◽  
Integral Equations ◽  
Branching Process ◽  
Branching Processes ◽  
Nonlinear Integral Equations ◽  
The Monte Carlo Method ◽  
The Mean

In this paper, we consider the Monte Carlo method for finding the solution of nonlinear integral equations at a fixed point xo‐ In this method, simulated Galton‐Watson branching process is employed for solving the proposed integral equation. The main goal of this paper is to compare the behavior of three classifications of branching process based on the mean progeny, i.e. the subcritical, critical and supercritical process.

scholarly journals Markov chain Monte Carlo method to solve Fredholm integral equations

2018 ◽  
Vol 22 (4) ◽  
pp. 1673-1678
Author(s):  
Yi Tian
Keyword(s):  
Integral Equation ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Method ◽  
Integral Equations ◽  
Fredholm Integral Equations ◽  
Thermal Problem ◽  
The Monte Carlo Method

A thermal problem can be always modeled using an integral equation. This paper uses the Monte Carlo method based on the simulation of a continuous Markov chain to solve Fredholm integral equations of the second kind. Some examples are given to show the efficiency of the present work.

scholarly journals The Reliability Model of Artificial Monitoring on the Anomalous Event in Expressway Tunnels and Monte Carlo Simulation

2019 ◽  
Vol 4 (3) ◽  
pp. p172
Author(s):  
Ling WU ◽  
Yueqi HU ◽  
Weihua ZHAO ◽  
Tong ZHU
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Video Surveillance ◽  
Warning System ◽  
Reliability Models ◽  
The Monte Carlo Method ◽  
Anomalous Event ◽  
Actual Operation ◽  
The Mean ◽  
Mean Time

Artificial monitoring remains to be a major way to detect anomalous events in expressway tunnels. To estimate the reliability of artificial monitoring on anomalous events in expressway tunnels, the video surveillance and mobile inspection based reliability models of artificial monitoring on the anomalous event in the expressway tunnel were built, and Monte Carlo method was applied to calculate the probability and mean time to detect the anomalous event at the specific time. The results showed that the Monte Carlo method could simulate video surveillance and mobile inspection, and obtain the probability distribution and mean time of detecting anomalous events. The mean time to spot the anomalous event was in reverse relation with the number of inspectors, the time of mobile inspection, and the reliability probability of the monitoring pre-warning system in tunnels and was in positive relationships with the departure interval. Combined with the actual operation cost, the model serves as a basis for the artificial monitoring package.

Estimation of Random Variable Distribution Parameters by the Monte Carlo Method

2013 ◽  
Vol 20 (2) ◽  
pp. 249-262 ◽  
Author(s):  
Sergiusz Sienkowski
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Random Variable ◽  
Statistical Parameters ◽  
The Monte Carlo Method ◽  
Variable Distribution ◽  
Distribution Parameters ◽  
The Subject ◽  
The Mean ◽  
Typical Measurement

Abstract The paper is concerned with issues of the estimation of random variable distribution parameters by the Monte Carlo method. Such quantities can correspond to statistical parameters computed based on the data obtained in typical measurement situations. The subject of the research is the mean, the mean square and the variance of random variables with uniform, Gaussian, Student, Simpson, trapezoidal, exponential, gamma and arcsine distributions.

scholarly journals The Existence and Uniqueness of the Solution of a Nonlinear Fredholm–Volterra Integral Equation with Modified Argument via Geraghty Contractions

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 29
Author(s):  
Maria Dobriţoiu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Nonlinear Integral Equations ◽  
Uniqueness Of The Solution

Using some of the extended fixed point results for Geraghty contractions in b-metric spaces given by Faraji, Savić and Radenović and their idea to apply these results to nonlinear integral equations, in this paper we present some existence and uniqueness conditions for the solution of a nonlinear Fredholm–Volterra integral equation with a modified argument.

A Boundary Element Method for Structural Reliability

2014 ◽  
Vol 627 ◽  
pp. 453-456 ◽  
Author(s):  
Xi Yong Huang ◽  
M.H. Aliabadi
Keyword(s):  
Integral Equation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Structural Reliability ◽  
Boundary Integral ◽  
The Monte Carlo Method ◽  
Derivatives Of ◽  
Element Method

In this paper a sensitivity formulation using the Boundary Element Method (BEM) is presentedfor analysis of structural reliability problems. The sensitivity formulation is based on implicit differentiation method where the first and second order derivatives of the random variables are obtained directly by differentiation of the discretised boundary integral equation. The structural reliability is assessed using the Monte Carlo Method and FORM with BEM sensitivity parameters. A benchmark example is presented to demonstrate the accuracy and efficiency of the BEM for both Monte Carlo and Sensitivity based FORM approaches.

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