Multivariate pade approximants and its applications

A variety of numerical methods are available for the solution of systems of differential equations. One of them is Padé approximants. It is known that Padé approximants are usually superior to many numerical methods. In this thesis, to show this superiority Padé approximants and Differential transform method(DTM) were compared. This comparison especially was made between two-dimensional transform method and multivariate Padé approximants. Some differential-algebraic equations(DAE ) and partial differential equations(PDE) were solved by using DTM. The unvariate and multivariate Padé approximants of this solutions were compared to solutions that found by DTM . As a result, it was seen that unvariate and multivariate Padé approximants are respectively superior to onedimensional and two-dimensional DTM. Keywords: Unvariate Padé approximants, Multivariate Padé approximants, One-dimensional differential transform method(DTM), Two-dimensional differential transform method(DTM), Partial differential equations(PDE), Differential-Algebraic equations(DAE).