The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called "jumps" is studied and asymptotic L 2 constants of the rate of convergence of the method are computed.

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Our objective with this paper is to discuss multi-switching problems, arising as variational inequalities, that models decision under uncertainty. We prove general existence theory through monotone scheme, and discuss iterative methods for numerical results. We also connect the recently developed models for asset bubbles (which is a non-local problem) to switching problems with two possible switching cases.

In the current work we consider the numerical solutions of equations of stationary states for a general class of the spatial segregation of reaction-diffusion systems with m ≥ 2 population densities. We introduce a discrete multi-phase minimization problem related to the segregation problem, which allows to prove the existence and uniqueness of the corresponding finite difference scheme. Based on that scheme, we suggest an iterative algorithm and show its consistency and stability. For the special case m = 2, we show that the problem gives rise to the generalized version of the so-called two-phase obstacle problem. In this particular case we introduce the notion of viscosity solutions and prove convergence of the difference scheme to the unique viscosity solution. At the end of the paper we present computational tests, for different internal dynamics, and discuss numerical results.2000 Mathematics Subject Classification. 35R35, 65N06, 65N22, 92D25.

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