Fast solvers of weakly singular integral equations of the second kind

Mathematical Modelling and Analysis

Gennadi Vainikko¹  Sumaira Rehman¹  Arvet Pedas¹ 

[1] University of Tartu,Institute of Mathematics and Statistics, J.Liivi 2, Tartu, Estonia;

关键词: Complexity;    Fast solvers;    Weakly singular integral equations;    Fredholm equations;    Periodization;    Trigonometric collocation;   

DOI  :  10.3846/mma.2018.039

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown