New approach to partial differential approximants

Abstract

The modellmg of physical phenomena usually results to nonlinear problems whose solutions may have singularities Practically tile locations of tile singularities are important for many problem" a solution can be Iuwld as a series in powers of one or ~everal independent variable" In this thesis under the title "A New Approach To Partial Differential ApprOXllnanto" we ha,e analysed series L11p<Jwer~ of lwo independent variable; hy HLgh-ordeLpartial differelltl1l1approxlInanls We have developed the method using the concepl or I'mk-Hel"lllJle c1a%, II consists of a high-order linear partial differenlial equation with polynomi~1 eoen"Lciems that is satlsfied appruxlmalely by the partial sum of the muhivariable po\\'er serie.1 We have also reviewed the different approximant methods lor the summation or series in powers of one or more Independent variables Our aml I, to apply the new method to problems in phy~icailield, patlicularly in fluid dynamics.