Two-point Padé approximants and their applications to in solving mechanical problems

This review article deals with two-point Padé approximants (TPPAs) and their applications to mechanics. The attention is paid to new applications of TPPAs such as: 1) Laplace transform inversion, 2) Matching of quasilinear and essentially nonlinear asymptotics, 3) Matching of expansions for high- and low-frequency oscillations, 4) Matching of limit asymptotics in the homogeimation problems, 5) TPPAs in the theory of composite materials, 6) TPPAs in the theory of nonlinear vibrations. The article deals also with one-point Padé approximants (PAs) and quasifractional approximants (QAs), which give possibility to overcome some TPPAs shortcomings.