عنوان

Constructive Methods for the Practical Treatment of Integral Equations

9783034893176

9783034899932

b406324

Constructive Methods for the Practical Treatment of Integral Equations

[Book]

Proceedings of the Conference Mathematisches Forschungsinstitut Oberwolfach, June 24-30, 1984 /

edited by G. Hämmerlin, K.-H. Hoffmann.

Basel :

Birkhäuser Basel,

1985.

International Series of Numerical Mathematics ;

73

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.

0

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 .

9783034899932

Springer eBooks

Science (General).

Hämmerlin, G.

Hoffmann, K.-H.

SpringerLink (Online service)

20190301080100.0

[Book]

Y