Methods and effective algorithms for solving multidimensional integral equations

Objectives. Integral equations have long been used in mathematical physics to demonstrate existence and uniqueness theorems for solving boundary value problems differential equations. However, despite integral a number of advantages comparison with corresponding where conditions are present the kernels equations, they rarely obtaining numerical solutions due presence dense matrices that arise when discretizing as opposed sparse case Recently, development computer technology methods computational mathematics, solution specific problems. In work, two two-dimensional three-dimensional proposed describing several significant classes physics.Methods. The method collocation on non-uniform uniform grids is discretize To obtain resulting systems linear algebraic (SLAEs), iterative used. grid, an efficient multiplying SLAE matrix by vector created.Results. Corresponding SLAEs considered set up. Efficient algorithms using fast Fourier transforms obtained grid.Conclusions. While grid can be describe complex domain configurations, there constraints dimensionality described systems. When orders magnitude higher; however, this case, it may difficult configuration domain. Selection particular depends problem available resources. Thus, preferable many problems, while