TY - JOUR
T1 - Expansion of solutions of parameterized equations and acceleration of numerical methods
AU - Gyöngy, István
AU - Krylov, Nicolai
PY - 2006
Y1 - 2006
N2 - A general scheme of parameterized families of equations is considered, and abstract results on the expansion of the solutions and on the acceleration of their convergence in terms of the parameter are presented. These results are applied to fractional step approximations for linear parabolic PDEs, systems of linear PDEs, and for nonlinear ordinary differential equations. Applications to accelerating the convergence of finite difference schemes for these equations will be presented in a subsequent paper.
AB - A general scheme of parameterized families of equations is considered, and abstract results on the expansion of the solutions and on the acceleration of their convergence in terms of the parameter are presented. These results are applied to fractional step approximations for linear parabolic PDEs, systems of linear PDEs, and for nonlinear ordinary differential equations. Applications to accelerating the convergence of finite difference schemes for these equations will be presented in a subsequent paper.
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U2 - 10.1215/ijm/1258059483
DO - 10.1215/ijm/1258059483
M3 - Article
AN - SCOPUS:33846819003
SN - 0019-2082
VL - 50
SP - 473
EP - 514
JO - Illinois Journal of Mathematics
JF - Illinois Journal of Mathematics
IS - 2
ER -