|
Consider a boundary value problem in a domain G with
a boundary dG. Monte Carlo methods are very efficient
for multidimensional problems in complicated domains.
There are two main Monte Carlo approaches for solving boundary value problems: Path integrals. This approach includes numerical shemes based on approximate calculation of path integrals representing the solution of the corresponding boundary value problem. Random walks. This approach is based on using a local integral representation of the solution for standard domains contained with the domain G (for example, a sphere, a ball, an elliposoide etc.). This leads to a Fredholm integral equation of the second type to be solved. The well known "random walk on grid points" can be considered in the framework of the first approach as such walks are discrete approximation of a random process. |
|