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 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.

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