Constructive Methods for the Practical Treatment of Integral Equations

Proceedings of the Conference at the Mathematisches Forschungsinstitut Oberwolfach, June 24-30, 1984
Erscheinungsjahr 2011
ISBN: 978-3-0348-9993-2
Verlag: Birkhäuser

Buch, Englisch, 284 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 547 g

Reihe: International Series of Numerical Mathematics

O I 1 -1 durch die GauB-Quadraturformel Q I n n L w 0 f (x 0) • i=1 1 1 Sei Rn: = I - Q das Fehlerfunktional. n Izl1, Fur eine im Kreis Kr I Kr: = {z E a: holomorphe Funktion f, f(z) = L i=O sei f i i • = x. ( 1. 1): = sup{ I a 0 I r i E:JN und R (qo) * O}, qo (x) o 1 n 1 1 In Xr:= {f: f holomorph in Kr und Iflr < oo} ist I. I eine Seminorm. Das Fehlerfunktional Rn ist in r (X I· I r) stetig I und fUr II Rn II I r, gilt die Identitat 00 (1. 2) L i=O Dieser Zugang zu ableitungsfreien Abschatzungen des Fehlerterms (1 • 3) geht auf Hammerlin [4] zurUck. 15 Erftillt die Gewichtsfunktion w eine der Bedingungen w (t ) w(t ) 1 2; (1. 4. a) w (-t ) w (-t ) 1 2 beziehungsweise w (t ) w(t ) 1 2 (1. 4. b) ~ w (-t ) w (-t ) 1 2 so gilt mit P (x) (X-X ) •. • (X-X ) ftir die Fehlernorm 1 n n r 1 Pn(x) (1. 5. a) --,-. - J w (x) dx Pn(r) -1 r-x beziehungsweise r 1 P (x) (1. 5. b) ( ) J w(x) ~ dx.

Zielgruppe

Research

Autoren/Hrsg.

Hämmerlin, G.

Hoffmann, K.H.

Inhaltsverzeichnis

Die Fehlernorm spezieller Gauss-Quadraturformeln.- Solving integral equations on surfaces in space.- An adaptive step size control for Volterra integral equations.- Concerning A(?)-stable mixed Volterra Runge-Kutta methods.- Constrained approximation techniques for solving integral equations.- On the numerical solution by collocation of Volterra integrodifferential equations with nonsmooth solutions.- Inclusion of regular and singular solutions of certain types of integral equations.- Two methods for solving the inverse scattering problem for time-harmonic acoustic waves.- Beyond superconvergence of collocation methods for Volterra integral equations of the first kind.- Optimal discrepancy principles for the Tikhonov regularization of integral equations of the first kind.- Spline-Galerkin method for solving some quantum mechanic integral equations.- Integral treatment of O.D.E with splines.- Product integration for weakly singular integral equations in ?m.- Stability results for discrete Volterra equations: Numerical experiments.- The design of acoustic torpedos.- On the condition number of boundary integral equations in acoustic scattering using combined double- and single-layer potentials.- Numerical solution of singular integral equations and an application to the theory of jet-flapped wings.- Tikhonov-Phillips regularization of the Radon Transform.- Numerical solution of a first kind Fredholm integral equation arising in electron-atom scattering.- Approximate solution of ill-posed equations: Arbitrarily slow convergence vs. superconvergence.- A unified analysis of discretization methods for Volterra-type equations.- Wiener-Hopf integral equations: Finite section approximation and projection methods.- Stability results for Abel equation.- Problems.