Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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01 Jan 1984TL;DR: Boundary element methods which can be considered as numerical or finite element approximations of boundary integral equations on closed boundary manifolds became very popular during the last years and correspondingly, a great variety of boundary value problems can now be solved numerically with corresponding boundary element programs as mentioned in this paper.
Abstract: Boundary element methods which can be considered as numerical or finite element approximations of boundary integral equations on closed boundary manifolds became very popular during the last years and, correspondingly,a great variety of boundary value problems can now be solved numerically with corresponding boundary element programs. Since the reduction of interior or exterior boundary value problems and also transmission problems to equivalent boundary integral equations is by no means a uniquely determined process — even for one specific boundary value problem — the growing number of applications has led to an enormous variety of mathematical problems and questions in connection with the applicability, correctness of formulations, systematical and computational errors and their estimation, computing times and expenses and efficiency.
4 citations
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TL;DR: In this paper, the authors studied the numerical solution of a reaction-diffusion system involving a reaction term of integral type arising from biological models and showed the existence and the asymptotic behavior of nonnegative numerical solutions.
Abstract: This paper presents the study of the numerical solution of a reaction-diffusion system involving a reaction term of integral type arising from biological models. By means of a monotone approach we introduce upper and lower solutions and then we show the existence and the asymptotic behavior of nonnegative numerical solutions. To this end, we require the positivity of the numerical scheme and so we can use some properties of positive and M-matrices. Finally we give some sufficient conditions to verify the asymptotic stability of the numerical solution.
4 citations
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3 citations