Buch, Englisch, Band 120, 362 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 1570 g
Buch, Englisch, Band 120, 362 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 1570 g
Reihe: International Series of Numerical Mathematics
ISBN: 978-3-7643-2871-9
Verlag: Springer
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
1 Introduction.- 1.1 Integral Equations.- 1.2 Basics from Analysis.- 1.3 Basics from Functional Analysis.- 1.4 Basics from Numerical Mathematics.- 2 Volterra Integral Equations.- 2.1 Theory of Volterra Integral Equations of the Second Kind.- 2.2 Numerical Solution by Quadrature Methods.- 2.3 Further Numerical Methods.- 2.4 Linear Volterra Integral Equations of Convolution Type.- 2.5 The Volterra Integral Equations of the First Kind.- 3 Theory of Fredholm Integral Equations of the Second Kind.- 3.1 The Fredholm Integral Equation of the Second Kind.- 3.2 Compactness of the Integral Operator K.- 3.3 Finite Approximability of the Integral Operator K.- 3.4 The Image Space of K.- 3.5 Solution of the Fredholm Integral Equation of the Second Kind.- 4 Numerical Treatment of Fredholm Integral Equations of the Second Kind.- 4.1 General Considerations.- 4.2 Discretisation by Kernel Approximation.- 4.3 Projection Methods in General.- 4.4 Collocation Method.- 4.5 Galerkin Method.- 4.6 Additional Comments Concerning Projection Methods.- 4.7 Discretisation by Quadrature: The Nyström Method.- 4.8 Supplements.- 5 Multi-Grid Methods for Solving Systems Arising from Integral Equations of the Second Kind.- 5.1 Preliminaries.- 5.2 Stability and Convergence (Discrete Formulation).- 5.3 The Hierarchy of Discrete Problems.- 5.4 Two-Grid Iteration.- 5.5 Multi-Grid Iteration.- 5.6 Nested Iteration.- 6 Abel’s Integral Equation.- 6.1 Notations and Examples.- 6.2 A Necessary Condition for a Bounded Solution.- 6.3 Euler’s Integrals.- 6.4 Inversion of Abel’s Integral Equation.- 6.5 Reformulation for Kernels k(x,y)/(x-y)?.- 6.6 Numerical Methods for Abel’s Integral Equation.- 7 Singular Integral Equations.- 7.1 The Cauchy Principal Value.- 7.2 The Cauchy Kernel.- 7.3 The Singular IntegralEquation.- 7.4 Application to the Dirichlet Problem for Laplace’s Equation.- 7.5 Hypersingular Integrals.- 8 The Integral Equation Method.- 8.1 The Single-Layer Potential.- 8.2 The Double-Layer Potential.- 8.3 The Hypersingular Integral Equation.- 8.4 Synopsis: Integral Equations for the Laplace Equation.- 8.5 The Integral Equation Method for Other Differential Equations.- 9 The Boundary Element Method.- 9.1 Construction of the Boundary Element Method.- 9.2 The Boundary Elements.- 9.3 Multi-Grid Methods.- 9.4 Integration and Numerical Quadrature.- 9.5 Solution of Inhomogeneous Equations.- 9.6 Computation of the Potential.- 9.7 The Panel Clustering Algorithm.