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Multivariate Padé approximation for solving partial differential equations (PDE). (English) Zbl 1219.65116
Summary: The numerical solution of partial differential equations (PDEs) by multivariate Padé approximations is considered. We applied these method to two examples. First, the PDE is converted to a power series by a two-dimensional differential transformation, Then the numerical solution of the equation is put into multivariate Padé series form. Thus we obtain a numerical solution of the PDE.
MSC:
65M80Fundamental solutions, Green’s function methods, etc. (IVP of PDE)
35L45First order hyperbolic systems, initial value problems
35L52Second-order hyperbolic systems, initial value problems
41A21Padé approximation
35C10Series solutions of PDE