Displaying similar documents to “Preface”

Verified numerical computations for large-scale linear systems

Katsuhisa Ozaki, Takeshi Terao, Takeshi Ogita, Takahiro Katagiri (2021)

Applications of Mathematics

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This paper concerns accuracy-guaranteed numerical computations for linear systems. Due to the rapid progress of supercomputers, the treatable problem size is getting larger. The larger the problem size, the more rounding errors in floating-point arithmetic can accumulate in general, and the more inaccurate numerical solutions are obtained. Therefore, it is important to verify the accuracy of numerical solutions. Verified numerical computations are used to produce error bounds on numerical...

Reliable numerical modelling of malaria propagation

István Faragó, Miklós Emil Mincsovics, Rahele Mosleh (2018)

Applications of Mathematics

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We investigate biological processes, particularly the propagation of malaria. Both the continuous and the numerical models on some fixed mesh should preserve the basic qualitative properties of the original phenomenon. Our main goal is to give the conditions for the discrete (numerical) models of the malaria phenomena under which they possess some given qualitative property, namely, to be between zero and one. The conditions which guarantee this requirement are related to the time-discretization...

Numerical integration in the Trefftz finite element method

Rozehnalová, Petra

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Using the high order Trefftz finite element method for solving partial differential equation requires numerical integration of oscillating functions. This integration could be performed, instead of classic techniques, also by the Levin method with some modifications. This paper shortly describes both the Trefftz method and the Levin method with its modification.

Adaptive mesh refinement strategy for a non conservative transport problem

Benjamin Aymard, Frédérique Clément, Marie Postel (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Long time simulations of transport equations raise computational challenges since they require both a large domain of calculation and sufficient accuracy. It is therefore advantageous, in terms of computational costs, to use a time varying adaptive mesh, with small cells in the region of interest and coarser cells where the solution is smooth. Biological models involving cell dynamics fall for instance within this framework and are often non conservative to account for cell division....

Numerical index with respect to an operator

Mohammad Ali Ardalani (2014)

Studia Mathematica

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We introduce new concepts of numerical range and numerical radius of one operator with respect to another one, which generalize in a natural way the known concepts of numerical range and numerical radius. We study basic properties of these new concepts and present some examples.