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Albert, G.E. and Meyer, M.A. (1956) Symposium of Monte Carlo Methods. A general Theory of Stochastic Estimates of the Neumann Series for Solution of Certain Fredholm Integral Equations and Related Series. Wiley, New York.

has been cited by the following article:

• 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.