River flooding is a problem of international interest. In the past few years many countries suffered from severe floods. A large part of the Netherlands is below sea level and river levels. The Dutch flood defences along the river Rhine are designed for water levels with a probability of...

We report on some numerical investigations on the chaotic behavior of certain spatial three- and four-body systems, subject to Newtonian gravitation. These configurations exhibit a new type of dynamics, mixing characteristics of the planar three-body problem and of the oscillatory motion...

Algorithms for estimating the integral over hyper-rectangular regions are discussed. Solving this problem in high dimensions is usually considered a domain of Monte Carlo and quasi-Monte Carlo methods, because their power degrades little with increasing dimension. These algorithms are compared...

Integrands that depend on a large number of equally important variables are considered and conditions that make expedient quasi-Monte Carlo integrations are investigated for dimensions n≤300.

We apply a new simulation scheme proposed by Kusuoka to finance problems. By using this method, we achieve 6500 times faster simulation than traditional Euler–Maruyama scheme.

A nonstandard finite difference scheme is constructed for the Burgers partial differential equation having no diffusion and a nonlinear logistic reaction term. This scheme preserves the positivity and boundedness properties of the original differential equation and includes the a priori...

Currently, in the context of quasi-Monte Carlo applications the most effective low-discrepancy sequences are digital (t, s)-sequences.