Padé-type approximation method for two dimensional Fredholm integral equations of the second kind

摘要

Two dimensional Fredholm integral equation of the second kind (2DF-II) on a bounded domain D is regarded as the problem with characteristic values. A two dimensional function-valued Padé-type approximation(2DFPTA) is defined. Its error formulas and convergence theorems are presented. To obtain higher order 2DFPTA, a determinantal expression and its recursive algorithm are given. In the end three numerical examples are tested, where one on the unit triangle of vertices (0; 0); (0; 1); (1; 0) and the other two on the square. The testing results show that 2DFPTA method is more accurate.