Stability and absolute stability of a three-point difference scheme

N. A. Chernyavskaya

doi:10.1016/S0898-1221(03)00083-X

Stability and absolute stability of a three-point difference scheme

N. A. Chernyavskaya

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Consider a three-point difference scheme -h^-2Δ⁽²⁾y_n + q_n(h)y_n = f_n(h), n ε Z = {0, ±1, ±2,...}. where h ε (0, h₀], h₀ is a given positive number, Δ⁽²⁾y_n = y_n+1 -2y_n + y_n-1, f(h) = {f_n(h)} n ε Z ε L_∞(h), L_∞(h) = {f(h) : ∥f(h)∥ L_∞(h) < ∞}, ∥f(h)∥ L_∞(h) = sup_nεZ|f_n(h)|. We assume a unique a priori requirement 0 ≤ q_n(h) < ∞ for any n ε Z and h ε (0, h₀]. The main results are a criterion of stability and absolute stability of the difference scheme (1) in the space L_∞(h).

Original language	English
Pages (from-to)	1181-1194
Number of pages	14
Journal	Computers and Mathematics with Applications
Volume	45
Issue number	6-9
DOIs	https://doi.org/10.1016/S0898-1221(03)00083-X
State	Published - 1 Mar 2003

Keywords

Absolute stability
Stability
Three-point difference scheme

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/S0898-1221(03)00083-X

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title = "Stability and absolute stability of a three-point difference scheme",

abstract = "Consider a three-point difference scheme -h-2Δ(2)yn + qn(h)yn = fn(h), n ε Z = {0, ±1, ±2,...}. where h ε (0, h0], h0 is a given positive number, Δ(2)yn = yn+1 -2yn + yn-1, f(h) = {fn(h)} n ε Z ε L∞(h), L∞(h) = {f(h) : ∥f(h)∥ L∞(h) < ∞}, ∥f(h)∥ L∞(h) = supnεZ|fn(h)|. We assume a unique a priori requirement 0 ≤ qn(h) < ∞ for any n ε Z and h ε (0, h0]. The main results are a criterion of stability and absolute stability of the difference scheme (1) in the space L∞(h).",

keywords = "Absolute stability, Stability, Three-point difference scheme",

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T1 - Stability and absolute stability of a three-point difference scheme

AU - Chernyavskaya, N. A.

PY - 2003/3/1

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N2 - Consider a three-point difference scheme -h-2Δ(2)yn + qn(h)yn = fn(h), n ε Z = {0, ±1, ±2,...}. where h ε (0, h0], h0 is a given positive number, Δ(2)yn = yn+1 -2yn + yn-1, f(h) = {fn(h)} n ε Z ε L∞(h), L∞(h) = {f(h) : ∥f(h)∥ L∞(h) < ∞}, ∥f(h)∥ L∞(h) = supnεZ|fn(h)|. We assume a unique a priori requirement 0 ≤ qn(h) < ∞ for any n ε Z and h ε (0, h0]. The main results are a criterion of stability and absolute stability of the difference scheme (1) in the space L∞(h).

AB - Consider a three-point difference scheme -h-2Δ(2)yn + qn(h)yn = fn(h), n ε Z = {0, ±1, ±2,...}. where h ε (0, h0], h0 is a given positive number, Δ(2)yn = yn+1 -2yn + yn-1, f(h) = {fn(h)} n ε Z ε L∞(h), L∞(h) = {f(h) : ∥f(h)∥ L∞(h) < ∞}, ∥f(h)∥ L∞(h) = supnεZ|fn(h)|. We assume a unique a priori requirement 0 ≤ qn(h) < ∞ for any n ε Z and h ε (0, h0]. The main results are a criterion of stability and absolute stability of the difference scheme (1) in the space L∞(h).

KW - Absolute stability

KW - Stability

KW - Three-point difference scheme

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JO - Computers and Mathematics with Applications

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IS - 6-9

ER -

Stability and absolute stability of a three-point difference scheme

Abstract

Keywords

ASJC Scopus subject areas

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