On 27 August at 13:30 Sumaira Rehman will defend her doctoral thesis “Fast and quasi-fast solvers for weakly singular Fredholm integral equations of the second kind” for obtaining the degree of Doctor of Philosophy (Mathematics).
Prof., Cand. Sc. Arvet Pedas, University of Tartu
Acad., Prof. Emer., D. Sc. Gennadi Vainikko, University of Tartu
Prof., Dr. Sergei V. Pereverzyev, Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences
Prof. Emer., Dr. Hab. Math. and Dr. Hab. Phys. Harijs Kalis, University of Latvia
In the present thesis the bounds of fast solving Fredholm integral equations of the second kind with a possible weak diagonal singularity of the kernel and certain boundary singularities of the derivatives of the free term has been discussed in a situation when the information about the smooth coefficient functions in the kernel and about the free term is restricted to a given number of their sample values. In a fast solver, the conditions of optimal accuracy and minimal arithmetical operations (complexity of the solver) are met. We mean the order optimality and order minimal work on a class of problems; the class of problems is defined by the smoothness conditions which have been set on the kernel and free term of the underlying problem.