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Harmonic averages, exact difference schemes and local Green’s functions in variable coefficient PDE problems

100%

Axelsson O., Karátson J.

Open Mathematics

2013

tom 11

nr 8

1441-1457

A brief survey is given to show that harmonic averages enter in a natural way in the numerical solution of various variable coefficient problems, such as in elliptic and transport equations, also of singular perturbation types. Local Green’s functions used as test functions in the Petrov-Galerkin finite element method combined with harmonic averages can be very efficient and are related to exact difference schemes.

Oscillations of difference equations with general advanced argument

100%

Chatzarakis G., Stavroulakis I.

Open Mathematics

2012

tom 10

nr 2

807-823

Consider the first order linear difference equation with general advanced argument and variable coefficients of the form $$\nabla x(n) - p(n)x(\tau (n)) = 0, n \geqslant 1,$$ where {p(n)} is a sequence of nonnegative real numbers, {τ(n)} is a sequence of positive integers such that $$\tau (n) \geqslant n + 1, n \geqslant 1,$$ and ▿ denotes the backward difference operator ▿x(n) = x(n) − x(n − 1). Sufficient conditions which guarantee that all solutions oscillate are established. Examples illustrating the results are given.

Ograniczanie wyników

2 Open Mathematics

1 Axelsson O.

1 Chatzarakis G.

1 Karátson J.

1 Stavroulakis I.

1 2013

1 2012

Wyniki wyszukiwania

Harmonic averages, exact difference schemes and local Green’s functions in variable coefficient PDE problems

Oscillations of difference equations with general advanced argument