What is the complexity of periodic weakly singular integral equations?
The authors construct a method for the numerical solution of Fredholm integral equations with weak singularities in spaces of periodic functions. The method is based on collocation principles using trigonometric functions. Both the computational complexity and the approximation error are studied in a very detailed way. This leads to the conclusion that, depending on the precise assumptions, the method is either fast (in the sense that the relation between complexity and error is of optimal order as the number of collocation points grows) or quasifast (in the sense that this relation differs from the optimal value only by a logarithmic, and hence slowly growing, term). Thus the complexity of the problem is the same as that for corresponding equations without singularities.
scientific article; zbMATH DE number 5343411
scientific article