FAST SOLVERS OF WEAKLY SINGULAR INTEGRAL EQUATIONS OF THE SECOND KIND | Zendy

Sumaira Rehman | Zendy; Arvet Pedas | Zendy; Gennadi Vainikko | Zendy

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FAST SOLVERS OF WEAKLY SINGULAR INTEGRAL EQUATIONS OF THE SECOND KIND

Author(s) -

Sumaira Rehman,

Arvet Pedas,

Gennadi Vainikko

Publication year - 2018

Publication title -

mathematical modelling and analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.491

H-Index - 25

eISSN - 1648-3510

pISSN - 1392-6292

DOI - 10.3846/mma.2018.039

Subject(s) - mathematics , singularity , gravitational singularity , kernel (algebra) , integral equation , mathematical analysis , diagonal , singular integral , term (time) , fredholm integral equation , boundary (topology) , solver , pure mathematics , mathematical optimization , geometry , physics , quantum mechanics

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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