This paper is concerned with the delay partial difference equation (1) where are real numbers, and are nonnegative integers, u is a positive integer. Sufficient and necessary conditions for all solutions of (1) to be oscillatory are obtained.
Asymptotic error expansions in the sense of -norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing...
In this paper we are concerned with finite element approximations to the evaluation of American options. First, following W. Allegretto etc., SIAM J. Numer. Anal. (2001), 834–857, we introduce a novel practical approach to the discussed problem, which involves the exact reformulation of the original problem and the implementation of the numerical solution over a very small region so that this algorithm is very rapid and highly accurate. Secondly by means of a superapproximation and interpolation...
In this paper we consider a parabolic inverse problem in which two unknown functions are involved in the boundary conditions, and attempt to recover these functions by measuring the values of the flux on the boundary. Explicit solutions for the temperature and the radiation terms are derived, and some stability and asymptotic results are discussed. Finally, by using the newly proposed numerical procedure some computational results are presented.
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