عنوان

Constructive Methods for the Practical Treatment of Integral Equations

(Number (ISBN

9783034893176

(Number (ISBN

9783034899932

Number

b406324

Title Proper

Constructive Methods for the Practical Treatment of Integral Equations

General Material Designation

[Book]

Other Title Information

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

First Statement of Responsibility

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

Place of Publication, Distribution, etc.

Basel :

Name of Publisher, Distributor, etc.

Birkhäuser Basel,

Date of Publication, Distribution, etc.

1985.

Series Title

International Series of Numerical Mathematics ;

Volume Designation

73

Text of Note

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

Text of Note

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 .

International Standard Book Number

9783034899932

Title

Springer eBooks

Science (General).

Hämmerlin, G.

Hoffmann, K.-H.

SpringerLink (Online service)

Date of Transaction

20190301080100.0

Electronic name

[Book]

Y