The optimal explicit unconditionally stable box scheme

Krzysztof Moszyński. "The optimal explicit unconditionally stable box scheme." Mathematica Applicanda 26.40 (1997): null. <http://eudml.org/doc/293207>.

@article{KrzysztofMoszyński1997,
abstract = {The finite difference “box” scheme, (see also [1],[2]), is considered on the simplest possible model of single first order linear hyperbolic equation: ut+mux=0 with constant, coefficient m, and one space variable. The optimal version of the scheme, which is nonoscilating and unconditionally stable with respect to the initial and boundary conditions, is derived in the class of box schemes of the order at, least one. If apropriately iterated, this ścinane may be applied to general systems of quasilinear first order hyperbolic equations in one space variable, as an explicit, unconditionally stable solver. For more than one space variable this solver is applicable via splitting (see [3]).},
author = {Krzysztof Moszyński},
journal = {Mathematica Applicanda},
keywords = {Finite difference methods; Stability and convergence of numerical methods},
language = {eng},
number = {40},
pages = {null},
title = {The optimal explicit unconditionally stable box scheme},
url = {http://eudml.org/doc/293207},
volume = {26},
year = {1997},
}

TY - JOUR
AU - Krzysztof Moszyński
TI - The optimal explicit unconditionally stable box scheme
JO - Mathematica Applicanda
PY - 1997
VL - 26
IS - 40
SP - null
AB - The finite difference “box” scheme, (see also [1],[2]), is considered on the simplest possible model of single first order linear hyperbolic equation: ut+mux=0 with constant, coefficient m, and one space variable. The optimal version of the scheme, which is nonoscilating and unconditionally stable with respect to the initial and boundary conditions, is derived in the class of box schemes of the order at, least one. If apropriately iterated, this ścinane may be applied to general systems of quasilinear first order hyperbolic equations in one space variable, as an explicit, unconditionally stable solver. For more than one space variable this solver is applicable via splitting (see [3]).
LA - eng
KW - Finite difference methods; Stability and convergence of numerical methods
UR - http://eudml.org/doc/293207
ER -