Systems of finite-part singular integral equations in Lp applied to crack problems

1994 ◽  
Vol 48 (2) ◽  
pp. 257-266 ◽  
Author(s):  
E.G. Ladopoulos
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Finite Part ◽  
Crack Problems

scholarly journals Numerical solution of integral equations with finite part integrals

1999 ◽  
Vol 22 (1) ◽  
pp. 155-160 ◽  
Author(s):  
Samir A. Ashour
Keyword(s):  
General Theory ◽  
Numerical Solution ◽  
Integral Equations ◽  
Singular Integral ◽  
Convergence Rates ◽  
Singular Integral Equations ◽  
Finite Part ◽  
Unbounded Operators

We obtain convergence rates for several algorithms that solve a class of Hadamard singular integral equations using the general theory of approximations for unbounded operators.

scholarly journals Finite-part singular integral approximations in Hilbert spaces

2004 ◽  
Vol 2004 (52) ◽  
pp. 2787-2793
Author(s):  
E. G. Ladopoulos ◽  
G. Tsamasphyros ◽  
V. A. Zisis
Keyword(s):  
Unit Circle ◽  
Integral Equations ◽  
Singular Integral ◽  
Hilbert Spaces ◽  
Existence Theorems ◽  
Singular Integral Equations ◽  
Finite Part ◽  
Algebraic Equations ◽  
Integration Interval ◽  
Linear Algebraic Equations

Some new approximation methods are proposed for the numerical evaluation of the finite-part singular integral equations defined on Hilbert spaces when their singularity consists of a homeomorphism of the integration interval, which is a unit circle, on itself. Therefore, some existence theorems are proved for the solutions of the finite-part singular integral equations, approximated by several systems of linear algebraic equations. The method is further extended for the proof of the existence of solutions for systems of finite-part singular integral equations defined on Hilbert spaces, when their singularity consists of a system of diffeomorphisms of the integration interval, which is a unit circle, on itself.

Sign in / Sign up

Export Citation Format

Share Document