caa a22 4500 469043539 CHVBK 20180323132817.0 cr unu---uuuuu 170328e19920701xx s 000 0 eng 10.1007/BF01195782 doi (NATIONALLICENCE)springer-10.1007/BF01195782 Spline approximation methods for multidimensional periodic pseudodifferential equations [Elektronische Daten] [S. Prössdorf, R. Schneider] We investigate several numerical methods for solving the pseudodifferential equationAu=f on the n-dimensional torusT n . We examine collocation methods as well as Galerkin-Petrov methods using various periodical spline functions. The considered spline spaces are subordinated to a uniform rectangular or triangular grid. For given approximation method and invertible pseudodifferential operatorA we compute a numerical symbolα C , resp.α G , depending onA and on the approximation method. It turns out that the stability of the numerical method is equivalent to the ellipticity of the corresponding numerical symbol. The case of variable symbols is tackled by a local principle. Optimal error estimates are established. Birkhäuser Verlag, 1992 Primary, 65R20 nationallicence Secondary, 35S05 nationallicence 45E05 nationallicence 45L10 nationallicence 47G30 nationallicence 65J10 nationallicence 65N30 nationallicence 65N35 nationallicence Prössdorf S. Karl-Weierstrass-Inst. für Math, Mohrenstr. 39, D-0 1086, Berlin aut Schneider R. Fachbereich Math. Technische Hochschule, Schlossgartenstr. 7, D-W 6100, Darmstadt aut Integral Equations and Operator Theory Birkhäuser-Verlag 15/4(1992-07-01), 626-672 0378-620X 15:4<626 1992 15 20 https://doi.org/10.1007/BF01195782 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01195782 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Prössdorf S. Karl-Weierstrass-Inst. für Math, Mohrenstr. 39, D-0 1086, Berlin aut NATIONALLICENCE 700 1- Schneider R. Fachbereich Math. Technische Hochschule, Schlossgartenstr. 7, D-W 6100, Darmstadt aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag 15/4(1992-07-01), 626-672 0378-620X 15:4<626 1992 15 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer