Report on the numerical experiments of Haselgrove’s method applied to the numerical solution of PDEs

Tomoaki Takemi and Shigeyoshi Ogawa

Mathematics and Computers in Simulation (MATCOM), 2003, vol. 62, issue 3, 539-552

Abstract: We are interested in the efficiency of the so called Haselgrove’s method (cf. [Math. Comp. 15 (76) (1961) 323; Math. Comp. 39 (160) (1982) 549]) for the evaluation of the multiple integral I=∫01∫01⋯∫01f(x1,x2,…,xp)dx1dx2⋯dxp.This is a kind of Monte Carlo method but different from it in two points:(1)procedure of taking arithmetic mean is improved,(2)employment the Weyl sequences, as random numbers, with a suitable set of irrational numbers.The precision of the usual Monte Carlo method is O(N−1/2), where N denotes the sample size, while it is O(N−r),r≥1 for Haselgrove’s method.

Keywords: Monte Carlo method; C.B. Haselgrove; Irrational number; Golden section number; Partial differential equation (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:62:y:2003:i:3:p:539-552

DOI: 10.1016/S0378-4754(02)00249-5

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