2011
DOI: 10.1002/fld.2305
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Multivariate padé approximation for solving partial differential equations (PDE)

Abstract: SUMMARYIn this paper, numerical solution of partial differential equations (PDEs) is considered by multivariate padé approximations. We applied these method to two examples. First, PDE has been converted to power series by two-dimensional differential transformation, Then the numerical solution of equation was put into multivariate padé series form. Thus, we obtained numerical solution of PDE.

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Cited by 11 publications
(10 citation statements)
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“…The principles and theory of the multivariate Padé approximation and its applicability for various of differential equations are given in [30][31][32][33][34][35][36][37][38][39][40] Let us now multiply jth row in p x and q x by x j m−1 j 2, ..., n 1 and afterwards divide jth column in p x and q x by x j−1 j 2, ..., n 1 . This results in a multiplication of numerator and denominator by x mn .…”
Section: Multivariate Padé Approximationmentioning
confidence: 99%
“…The principles and theory of the multivariate Padé approximation and its applicability for various of differential equations are given in [30][31][32][33][34][35][36][37][38][39][40] Let us now multiply jth row in p x and q x by x j m−1 j 2, ..., n 1 and afterwards divide jth column in p x and q x by x j−1 j 2, ..., n 1 . This results in a multiplication of numerator and denominator by x mn .…”
Section: Multivariate Padé Approximationmentioning
confidence: 99%
“…In recent times, univariate and multivariate padé approximaton have been succesfully applied to various problems in physical and engineering sciences [1][2][3][4][5]. "Padé approximant represents a function by the ratio of two polynomials.…”
Section: Introductionmentioning
confidence: 99%
“…In recent times,univariate and multivariate Padé approximation have been successfully applied to various problems in physical and engineering sciences [1][2][3][4][5][6][7]. As it is indicated in [16] "a Padé approximation can be far more accurate than a Taylor approximation.…”
Section: Introductionmentioning
confidence: 99%