Fast solvers of weakly singular integral equations of the second kind

We discuss the bounds of fast solving weakly singular Fredholm integral equations of the second kind with a possible diagonal singularity of the kernel and certain boundary singularities of the derivatives of the free term when the information about the smooth coefficient functions in the kernel and...

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Published inMathematical modelling and analysis Vol. 23; no. 4; pp. 639 - 664
Main Authors Rehman, Sumaira, Pedas, Arvet, Vainikko, Gennadi
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 09.10.2018
Subjects
Coefficients
Complexity
Derivatives (Mathematics)
Fast solvers
Fredholm equations
Integral equations
Kernel functions
Kernels
Mathematical analysis
Mathematical research
Measurement
Periodization
Singular integral equations
Singularities (Mathematics)
Singularity (mathematics)
Solvers
Trigonometric collocation
Weakly singular integral equations
Periodization
Weakly singular integral equations
Trigonometric collocation
Fast solvers
Fredholm equations
Complexity
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Summary:We discuss the bounds of fast solving weakly singular Fredholm integral equations of the second kind with a possible diagonal singularity of the kernel and certain boundary singularities of the derivatives of the free term when the information about the smooth coefficient functions in the kernel and about the free term is restricted to a given number of sample values. In this situation, a fast/quasifast solver is constructed. Thus the complexity of weakly singular integral equations occurs to be close to that of equations with smooth data without singularities. Our construction of fast/quasifast solvers is based on the periodization of the problem.
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ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2018.039