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

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.