Random Walks for Solving Boundary-Value Problems with Flux Conditions

@inproceedings{Simonov2006RandomWF,
  title={Random Walks for Solving Boundary-Value Problems with Flux Conditions},
  author={Nikolai A. Simonov},
  booktitle={Numerical Methods and Applications},
  year={2006}
}
We consider boundary-value problems for elliptic equations with constant coefficients and apply Monte Carlo methods to solving these equations. To take into account boundary conditions involving solution’s normal derivative, we apply the new mean-value relation written down at boundary point. This integral relation is exact and provides a possibility to get rid of the bias caused by usually used finite-difference approximation. We consider Neumann and mixed boundary-value problems, and also the… CONTINUE READING

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