TITLE:
On Solving a System of Volterra Integral Equations with Relaxed Monte Carlo Method
AUTHORS:
Zhimin Hong, Xiangzhong Fang, Zaizai Yan, Hui Hao
KEYWORDS:
Systems of Volterra Integral Equations, Quadrature Formula, Relaxed Monte Carlo Method, Importance Sampling
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.7,
July
25,
2016
ABSTRACT: A random simulation method was used for treatment of systems of Volterra
integral equations of the second kind. Firstly, a linear algebra system was
obtained by discretization using quadrature formula. Secondly, this algebra
system was solved by using relaxed Monte Carlo method with importance sampling and
numerical approximation solutions of the integral equations system were
achieved. It is theoretically proved that the validity of relaxed Monte Carlo
method is based on importance sampling to solve the integral equations system.
Finally, some numerical examples from literatures are given to show the
efficiency of the method.