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Variation of product function and numerical solution of some partial differential equations by low-discrepancy sequences

In this paper, we study two problems in quasi-Monte Carlo methods and their applications, the variation of the product of functions of bounded variation and the numerical solution of partial differential equations by low-discrepancy sequences. We give an inequality on the variation of the product of two functions of bounded variation and as an application we show that any low-discrepancy sequence can be used in the method of Hua and Wang (see [3]) to give an approximate solution of Cauchy's initial value problem for a class of parabolic partial differential equations.