THE APPROXIMATION SOLUTIONS FOR HIGHER DIMENSIONAL INTEGRO-DIFFERENTIAL EQUATIONS

This work deals with approximation solutions to a type of integro-differential equations in several complex variables.It concerns the Cauchy formula on higher dimensional domains.In our study,we make use of multiple power series expansions and an iterative computation method to solve a kind of integro-differential equation.We introduce a symmetrized topology product area which is called a bicylinder.We expand functions and derivatives of them to power series.Moreover we obtain unknown functions by comparing coefficients of the series on both sides of equations.We express the approximation solutions by a regular product of matrixes.