Unique solvability of restrictive Padé and restrictive Taylor's approximations

摘要

From 1995 to 2002 the author and others succeeded to apply a new approach for approximation which called restrictive Padé approximation and restrictive Taylor approximation. Almost the work is summarized in the nine papers [J. Faculty Educat. (1995) 63; Int. J. Comput. Math. 66 (1998) 343; Int. J. Comput. Math. 72 (1999) 271; Int. J. Comput. Math. 77 (2000) 251; J. Inst. Math. Comput. Sci. 11 (1) (2000) 63; J. Inst. Math. Comput. Sci. India 11 (2) (2000) 159; Int. J. Comput. Math. 78 (2001) 73; Int. J. Inst. Math. Comput. Sci. 12 (2) (2001) 153; Int. J. Comput. Math. 79 (5) (2002) 603]. It gives a lot of highly accurate, efficient and distinguished finite difference methods for numerical solutions of initial-boundary-value problems for parabolic and hyperbolic partial differential equations.Now this paper derived a general theory for solvability and uniqueness of the mentioned restrictive Padé and restrictive Taylor's approximations. A survey of the individual necessary and sufficient solvability and uniqueness conditions for several 15 examples of these approximations are given.