Quasi-random walks on balls using C.U.D. sequences

Authors:
Aneta Karaivanova;Hongmei Chi;Todor Gurov
Affiliations:
IPP, Bulgarian Academy of Sciences, Sofia, Bulgaria;Dept. of Computer & Information Sciences, Florida A&M University, Tallahassee, FL;IPP, Bulgarian Academy of Sciences, Sofia, Bulgaria
Venue:
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
Year:
2006

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Abstract

This paper presents work on solving elliptic BVPs problems based on quasi-random walks, by using a subset of uniformly distributed sequences--completely uniformly distributed (c.u.d.) sequences. This approach is novel for solving elliptic boundary value problems. The enhanced uniformity of c.u.d. sequences leads to faster convergence. We demonstrate that c.u.d. sequences can be a viable alternative to pseudo-random numbers when solving elliptic boundary value problems. Analysis of a simple problem in this paper showed that c.u.d. sequences achieve better numerical results than pseudorandom numbers, but also have the potential to converge faster and so reduce the computational burden.