Modifications of some first kind integral equations with logarithmic kernel to improve numerical conditioning

DOI10.1007/BF02253319zbMath0551.65093OpenAlexW73160570MaRDI QIDQ800708

Søren Christiansen

Publication date: 1985

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02253319

zbMATH Keywords

condition numbercollocation methodsscalingsingular valuesmatrix normspair of integral equations

Mathematics Subject Classification ID

Systems of singular linear integral equations (45F15) Numerical methods for integral equations (65R20) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items

Computation of the singular value expansion, Degenerate scale for 2D Laplace equation with mixed boundary condition and comparison with other conditions on the boundary, An asymptotic property of degenerate scales for multiple holes in plane elasticity, First kind integral equations for the numerical solution of the plane Dirichlet problem

Uses Software

• IMSL Numerical Libraries

Cites Work

• On the stability of integral equations of the first kind with logarithmic kernels
• A finite element method for some integral equations of the first kind
• Numerical mapping of exterior domains
• Some applications of a galerkin‐collocation method for boundary integral equations of the first kind
• On the condition number of the influence matrix belonging to some first kind integral equations with logarithmic kernel
• Condition number of matrices derived from two classes of integral equations
• Integral Equations without a Unique Solution can be made Useful for Solving some Plane Harmonic Problems
• Numerical solution of an integral equation with a logarithmic kernel
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