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1D and 2D finite-difference operators for periodic functions on arbitrary mesh

Sobczyk Tadeusz Jan

Archives of Electrical Engineering

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2022

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Vol. 71, nr 1

265--275

EN

This paper presents novel discrete differential operators for periodic functions of one- and two-variables, which relate the values of the derivatives to the values of the function itself for a set of arbitrarily chosen points over the function’s area. It is very characteristic, that the values of the derivatives at each point depend on the function values at all points in that area. Such operators allow one to easily create finite-difference equations for boundaryvalue problems. The operators are addressed especially to nonlinear differential equations.

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Subadditive periodic functions

Matkowski J.

Opuscula Mathematica

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2011

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Vol. 31, no. 1

75-96

EN

Some conditions under which any subadditive function is periodic are presented. It is shown that the boundedness from below in a neighborhood of a point of a subadditive periodic (s.p.) function implies its nonnegativity, and the boundedness from above in a neighborhood of a point implies it nonnegativity and global boundedness from above. A necessary and sufficient condition for existence of a subadditive periodic extension of a function ƒ0 : [0, 1) ? R is given. The continuity, differentiability of a s.p. function is discussed, and an example of a continuous nowhere differentiable s.p. function is presented. The functions which are the sums of linear functions and s.p. functions are characterized. The refinements of some known results on the continuity of subadditive functions are presented.

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About definition of a periodic function

Rygał G., Bryll G.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2007

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Vol. 12

375-380

EN

In this paper we consider various definitions of a periodic function and establish connections between them, in particular, we prove equivalence of some of them. In papers and textbooks one can find different definitions of a periodic function. This raises the question which of them are equivalent.

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